From 4408460de1dbda4d4e75f08574d9c59bf1f5f16b Mon Sep 17 00:00:00 2001
From: lbarasti <lbarasti@users.noreply.github.com>
Date: Mon, 13 Apr 2020 20:50:32 +0100
Subject: [PATCH] Update version and docs

---
 docs/Statistics.html                          |  63 +--
 docs/Statistics/Distributions.html            |  17 +-
 docs/Statistics/Distributions/Bernoulli.html  | 392 ++++++++++++++++++
 docs/Statistics/Distributions/Constant.html   |  75 +++-
 .../Distributions/ContinuousDistribution.html | 292 +++++++++++++
 .../Distributions/DiscreteDistribution.html   | 292 +++++++++++++
 .../Distributions/Distribution.html           |  29 +-
 .../Statistics/Distributions/Exponential.html |  75 +++-
 docs/Statistics/Distributions/Normal.html     |  88 +++-
 docs/Statistics/Distributions/Poisson.html    |  75 +++-
 docs/Statistics/Distributions/Uniform.html    |  75 +++-
 docs/index.html                               |  15 +
 docs/index.json                               |   2 +-
 docs/search-index.js                          |   2 +-
 shard.yml                                     |   2 +-
 src/statistics.cr                             |   2 +-
 16 files changed, 1433 insertions(+), 63 deletions(-)
 create mode 100644 docs/Statistics/Distributions/Bernoulli.html
 create mode 100644 docs/Statistics/Distributions/ContinuousDistribution.html
 create mode 100644 docs/Statistics/Distributions/DiscreteDistribution.html

diff --git a/docs/Statistics.html b/docs/Statistics.html
index d6b3142..672a6f7 100644
--- a/docs/Statistics.html
+++ b/docs/Statistics.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -157,14 +172,14 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L1" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L1" target="_blank">
         lib/distributions.cr
       </a>
     
     <br/>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L6" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L6" target="_blank">
         statistics.cr
       </a>
     
@@ -186,7 +201,7 @@ <h2>
   <dl>
     
       <dt class="entry-const" id="VERSION">
-        <strong>VERSION</strong> = <code><span class="s">&quot;0.3.0&quot;</span></code>
+        <strong>VERSION</strong> = <code><span class="s">&quot;1.0.0&quot;</span></code>
       </dt>
       
     
@@ -209,7 +224,7 @@ <h2>
   <ul class="list-summary">
     
       <li class="entry-summary">
-        <a href="#bin_count(values:Enumerable,bins:Int32,min=nil,max=nil):Array(::Tuple(Float64,Int32))-instance-method" class="signature"><strong>#bin_count</strong>(values : Enumerable, bins : Int32, min = <span class="n">nil</span>, max = <span class="n">nil</span>) : Array(::Tuple(Float64, Int32))</a>
+        <a href="#bin_count(values:Enumerable,bins:Int32,min=nil,max=nil,edge:Edge=:left):Bins-instance-method" class="signature"><strong>#bin_count</strong>(values : Enumerable, bins : Int32, min = <span class="n">nil</span>, max = <span class="n">nil</span>, edge : Edge = <span class="n">:left</span>) : Bins</a>
         
           <div class="summary"><p>Counts the number of values in each bin of size <code>(max - min) / bins</code>.</p></div>
         
@@ -330,32 +345,32 @@ <h2>
     Instance Method Detail
   </h2>
   
-    <div class="entry-detail" id="bin_count(values:Enumerable,bins:Int32,min=nil,max=nil):Array(::Tuple(Float64,Int32))-instance-method">
+    <div class="entry-detail" id="bin_count(values:Enumerable,bins:Int32,min=nil,max=nil,edge:Edge=:left):Bins-instance-method">
       <div class="signature">
         
-        def <strong>bin_count</strong>(values : Enumerable, bins : Int32, min = <span class="n">nil</span>, max = <span class="n">nil</span>) : Array(::Tuple(Float64, Int32))
+        def <strong>bin_count</strong>(values : Enumerable, bins : Int32, min = <span class="n">nil</span>, max = <span class="n">nil</span>, edge : Edge = <span class="n">:left</span>) : Bins
 
-        <a class="method-permalink" href="#bin_count(values:Enumerable,bins:Int32,min=nil,max=nil):Array(::Tuple(Float64,Int32))-instance-method">#</a>
+        <a class="method-permalink" href="#bin_count(values:Enumerable,bins:Int32,min=nil,max=nil,edge:Edge=:left):Bins-instance-method">#</a>
       </div>
       
         <div class="doc">
           
           <p>Counts the number of values in each bin of size <code>(max - min) / bins</code>.</p>
 
-<p>Returns an array of tuples <code>{edge, count}</code> ordered by <code>edge</code>, where <code>edge</code> is the
-starting edge of a bin and <code>count</code> is the number of values in the corresponding <code>bin</code>.</p>
+<p>Returns a <code>Bins</code> object where <code>edges</code> and <code>counts</code> are ordered by edge.</p>
 
 <p><span class="flag purple">NOTE</span>  Any empty bin will also be included.</p>
 
 <p>Parameters</p>
 
-<ul><li>values: a one-dimensional dataset.</li><li>bins: the number of equally-sized bins to divide the datapoints into.</li><li>min: the left end of the first bin's edge. If none is provided, then <code>values.min</code> is used.</li><li>max: the right end of the last bin's edge. If none is provided, then <code>values.max</code> is used.</li></ul>
+<ul><li>values: a one-dimensional dataset.</li><li>bins: the number of equally-sized bins to divide the datapoints into.</li><li>min: the left end of the first bin's edge. If none is provided, then <code>values.min</code> is used.</li><li>max: the right end of the last bin's edge. If none is provided, then <code>values.max</code> is used.</li><li>edge: determines whether the left edge of the bin, its mid-point or right edge should be returned.
+  Choices are <code>:left</code>, <code>:centre</code> and <code>:right</code>. Default is <code>:left</code>.</li></ul>
         </div>
       
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L57" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L67" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -380,7 +395,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L14" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L14" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -407,7 +422,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L38" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L38" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -434,7 +449,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L84" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L105" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -459,7 +474,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L103" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L124" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -489,7 +504,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L117" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L138" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -510,7 +525,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L142" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L163" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -538,7 +553,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L136" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L157" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -568,7 +583,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L154" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L175" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -594,7 +609,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L165" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L186" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -624,7 +639,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L181" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L202" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -651,7 +666,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L201" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L222" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -679,7 +694,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L219" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L240" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -707,7 +722,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L232" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L253" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Statistics/Distributions.html b/docs/Statistics/Distributions.html
index 9d9ff0a..d343a93 100644
--- a/docs/Statistics/Distributions.html
+++ b/docs/Statistics/Distributions.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="../Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="../Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -130,7 +145,7 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L2" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L2" target="_blank">
         lib/distributions.cr
       </a>
     
diff --git a/docs/Statistics/Distributions/Bernoulli.html b/docs/Statistics/Distributions/Bernoulli.html
new file mode 100644
index 0000000..3f1a499
--- /dev/null
+++ b/docs/Statistics/Distributions/Bernoulli.html
@@ -0,0 +1,392 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="utf-8" />
+<meta http-equiv="X-UA-Compatible" content="IE=edge">
+<meta name="generator" content="Crystal Docs 0.33.0">
+
+<link href="../../css/style.css" rel="stylesheet" type="text/css" />
+<script type="text/javascript" src="../../js/doc.js"></script>
+
+<svg class="hidden">
+  <symbol id="octicon-link" viewBox="0 0 16 16">
+    <path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path>
+  </symbol>
+</svg>
+
+  <meta id="repository-name" content="github.com/lbarasti/statistics">
+  <title>Statistics::Distributions::Bernoulli - github.com/lbarasti/statistics</title>
+  <script type="text/javascript">
+    CrystalDoc.base_path = "../../";
+  </script>
+</head>
+<body>
+
+<div class="sidebar">
+  <div class="sidebar-header">
+    <div class="search-box">
+      <input type="search" class="search-input" placeholder="Search..." spellcheck="false" aria-label="Search">
+    </div>
+
+    <div class="repository-links">
+      <a href="../../index.html">README</a>
+    </div>
+  </div>
+
+  <div class="search-results" class="hidden">
+    <ul class="search-list"></ul>
+  </div>
+
+  <div class="types-list">
+    <ul>
+  
+  <li class="parent open current" data-id="github.com/lbarasti/statistics/Statistics" data-name="statistics">
+      <a href="../../Statistics.html">Statistics</a>
+      
+        <ul>
+  
+  <li class="parent open current" data-id="github.com/lbarasti/statistics/Statistics/Distributions" data-name="statistics::distributions">
+      <a href="../../Statistics/Distributions.html">Distributions</a>
+      
+        <ul>
+  
+  <li class=" current" data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
+      <a href="../../Statistics/Distributions/Constant.html">Constant</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
+      <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Exponential" data-name="statistics::distributions::exponential">
+      <a href="../../Statistics/Distributions/Exponential.html">Exponential</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Normal" data-name="statistics::distributions::normal">
+      <a href="../../Statistics/Distributions/Normal.html">Normal</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Poisson" data-name="statistics::distributions::poisson">
+      <a href="../../Statistics/Distributions/Poisson.html">Poisson</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Uniform" data-name="statistics::distributions::uniform">
+      <a href="../../Statistics/Distributions/Uniform.html">Uniform</a>
+      
+    </li>
+  
+</ul>
+
+      
+    </li>
+  
+</ul>
+
+      
+    </li>
+  
+</ul>
+
+  </div>
+</div>
+
+
+<div class="main-content">
+<h1 class="type-name">
+
+  <span class="kind">class</span> Statistics::Distributions::Bernoulli
+
+</h1>
+
+
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Bernoulli.html">Statistics::Distributions::Bernoulli</a></li><li class="superclass"><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Int32)</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Int32)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+
+
+
+
+  <h2>
+    <a id="overview" class="anchor" href="#overview">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Overview
+  </h2>
+
+  <p>The discrete probability distribution of a random variable which takes
+the value 1 with probability <code>p</code> and the value 0 with probability
+<code>q=1-p</code> (source: <a href="https://en.wikipedia.org/wiki/Bernoulli_distribution" target="_blank">wikipedia</a>).</p>
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+  <h2>
+    <a id="defined-in" class="anchor" href="#defined-in">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Defined in:
+  </h2>
+  
+    
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L23" target="_blank">
+        lib/distributions.cr
+      </a>
+    
+    <br/>
+  
+
+
+
+
+
+  <h2>
+    <a id="constructors" class="anchor" href="#constructors">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Constructors
+  </h2>
+  <ul class="list-summary">
+    
+      <li class="entry-summary">
+        <a href="#new(p:Float64)-class-method" class="signature"><strong>.new</strong>(p : Float64)</a>
+        
+          <div class="summary"><p>Creates Bernoulli distribution with success rate <code>p</code>.</p></div>
+        
+      </li>
+    
+  </ul>
+
+
+
+
+
+  <h2>
+    <a id="instance-method-summary" class="anchor" href="#instance-method-summary">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Instance Method Summary
+  </h2>
+  <ul class="list-summary">
+    
+      <li class="entry-summary">
+        <a href="#pmf(x)-instance-method" class="signature"><strong>#pmf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Mass Function (PMF) of a discrete random variable.</p></div>
+        
+      </li>
+    
+      <li class="entry-summary">
+        <a href="#rand:Int32-instance-method" class="signature"><strong>#rand</strong> : Int32</a>
+        
+          <div class="summary"><p>Samples a random variable with the given distribution.</p></div>
+        
+      </li>
+    
+  </ul>
+
+
+
+
+
+<div class="methods-inherited">
+  
+    
+
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Int32)</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/DiscreteDistribution.html#pmf(x)-instance-method" class="tooltip">
+      <span>pmf(x)</span>
+    pmf</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Int32)</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/Distribution.html#rand:T-instance-method" class="tooltip">
+      <span>rand : T</span>
+    rand</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
+
+    
+
+
+    
+
+
+  
+    
+
+
+    
+
+
+    
+
+
+  
+</div>
+
+
+  <h2>
+    <a id="constructor-detail" class="anchor" href="#constructor-detail">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Constructor Detail
+  </h2>
+  
+    <div class="entry-detail" id="new(p:Float64)-class-method">
+      <div class="signature">
+        
+        def self.<strong>new</strong>(p : Float64)
+
+        <a class="method-permalink" href="#new(p:Float64)-class-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+          <p>Creates Bernoulli distribution with success rate <code>p</code>.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L25" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+
+
+
+
+
+  <h2>
+    <a id="instance-method-detail" class="anchor" href="#instance-method-detail">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Instance Method Detail
+  </h2>
+  
+    <div class="entry-detail" id="pmf(x)-instance-method">
+      <div class="signature">
+        
+        def <strong>pmf</strong>(x)
+
+        <a class="method-permalink" href="#pmf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+            <div class="doc-inherited">
+              Description copied from class <a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Int32)</a>
+            </div>
+          
+          <p>The Probability Mass Function (PMF) of a discrete
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L28" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="rand:Int32-instance-method">
+      <div class="signature">
+        
+        def <strong>rand</strong> : Int32
+
+        <a class="method-permalink" href="#rand:Int32-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+            <div class="doc-inherited">
+              Description copied from class <a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Int32)</a>
+            </div>
+          
+          <p>Samples a random variable with the given distribution.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L36" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+
+
+
+
+</div>
+
+</body>
+</html>
diff --git a/docs/Statistics/Distributions/Constant.html b/docs/Statistics/Distributions/Constant.html
index 70d4610..940c78a 100644
--- a/docs/Statistics/Distributions/Constant.html
+++ b/docs/Statistics/Distributions/Constant.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" current" data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="../../Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -104,7 +119,7 @@ <h1 class="type-name">
 </h1>
 
 
-  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Constant.html">Statistics::Distributions::Constant</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Constant.html">Statistics::Distributions::Constant</a></li><li class="superclass"><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Float64)</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
 
 
 
@@ -143,7 +158,7 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L9" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L42" target="_blank">
         lib/distributions.cr
       </a>
     
@@ -187,6 +202,13 @@ <h2>
   </h2>
   <ul class="list-summary">
     
+      <li class="entry-summary">
+        <a href="#pmf(x)-instance-method" class="signature"><strong>#pmf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Mass Function (PMF) of a discrete random variable.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#rand:Float64-instance-method" class="signature"><strong>#rand</strong> : Float64</a>
         
@@ -204,6 +226,25 @@ <h2>
   
     
 
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Float64)</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/DiscreteDistribution.html#pmf(x)-instance-method" class="tooltip">
+      <span>pmf(x)</span>
+    pmf</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
   <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></code></h3>
   
   
@@ -269,7 +310,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L13" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L50" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -288,6 +329,32 @@ <h2>
     Instance Method Detail
   </h2>
   
+    <div class="entry-detail" id="pmf(x)-instance-method">
+      <div class="signature">
+        
+        def <strong>pmf</strong>(x)
+
+        <a class="method-permalink" href="#pmf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+            <div class="doc-inherited">
+              Description copied from class <a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Float64)</a>
+            </div>
+          
+          <p>The Probability Mass Function (PMF) of a discrete
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L45" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
     <div class="entry-detail" id="rand:Float64-instance-method">
       <div class="signature">
         
@@ -308,7 +375,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L10" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L43" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Statistics/Distributions/ContinuousDistribution.html b/docs/Statistics/Distributions/ContinuousDistribution.html
new file mode 100644
index 0000000..8ff4721
--- /dev/null
+++ b/docs/Statistics/Distributions/ContinuousDistribution.html
@@ -0,0 +1,292 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="utf-8" />
+<meta http-equiv="X-UA-Compatible" content="IE=edge">
+<meta name="generator" content="Crystal Docs 0.33.0">
+
+<link href="../../css/style.css" rel="stylesheet" type="text/css" />
+<script type="text/javascript" src="../../js/doc.js"></script>
+
+<svg class="hidden">
+  <symbol id="octicon-link" viewBox="0 0 16 16">
+    <path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path>
+  </symbol>
+</svg>
+
+  <meta id="repository-name" content="github.com/lbarasti/statistics">
+  <title>Statistics::Distributions::ContinuousDistribution - github.com/lbarasti/statistics</title>
+  <script type="text/javascript">
+    CrystalDoc.base_path = "../../";
+  </script>
+</head>
+<body>
+
+<div class="sidebar">
+  <div class="sidebar-header">
+    <div class="search-box">
+      <input type="search" class="search-input" placeholder="Search..." spellcheck="false" aria-label="Search">
+    </div>
+
+    <div class="repository-links">
+      <a href="../../index.html">README</a>
+    </div>
+  </div>
+
+  <div class="search-results" class="hidden">
+    <ul class="search-list"></ul>
+  </div>
+
+  <div class="types-list">
+    <ul>
+  
+  <li class="parent open current" data-id="github.com/lbarasti/statistics/Statistics" data-name="statistics">
+      <a href="../../Statistics.html">Statistics</a>
+      
+        <ul>
+  
+  <li class="parent open current" data-id="github.com/lbarasti/statistics/Statistics/Distributions" data-name="statistics::distributions">
+      <a href="../../Statistics/Distributions.html">Distributions</a>
+      
+        <ul>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
+      <a href="../../Statistics/Distributions/Constant.html">Constant</a>
+      
+    </li>
+  
+  <li class=" current" data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
+      <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Exponential" data-name="statistics::distributions::exponential">
+      <a href="../../Statistics/Distributions/Exponential.html">Exponential</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Normal" data-name="statistics::distributions::normal">
+      <a href="../../Statistics/Distributions/Normal.html">Normal</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Poisson" data-name="statistics::distributions::poisson">
+      <a href="../../Statistics/Distributions/Poisson.html">Poisson</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Uniform" data-name="statistics::distributions::uniform">
+      <a href="../../Statistics/Distributions/Uniform.html">Uniform</a>
+      
+    </li>
+  
+</ul>
+
+      
+    </li>
+  
+</ul>
+
+      
+    </li>
+  
+</ul>
+
+  </div>
+</div>
+
+
+<div class="main-content">
+<h1 class="type-name">
+
+  <span class="kind">abstract class</span> Statistics::Distributions::ContinuousDistribution
+
+</h1>
+
+
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+
+
+
+
+
+
+
+
+
+
+
+
+  <h2>
+    <a id="direct-known-subclasses" class="anchor" href="#direct-known-subclasses">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Direct Known Subclasses
+  </h2>
+  <ul class="other-types-list">
+    
+      <li class="other-type"><a href="../../Statistics/Distributions/Exponential.html">Statistics::Distributions::Exponential</a></li>
+    
+      <li class="other-type"><a href="../../Statistics/Distributions/Normal.html">Statistics::Distributions::Normal</a></li>
+    
+      <li class="other-type"><a href="../../Statistics/Distributions/Uniform.html">Statistics::Distributions::Uniform</a></li>
+    
+  </ul>
+
+
+
+
+
+
+  <h2>
+    <a id="defined-in" class="anchor" href="#defined-in">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Defined in:
+  </h2>
+  
+    
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L14" target="_blank">
+        lib/distributions.cr
+      </a>
+    
+    <br/>
+  
+
+
+
+
+
+
+
+
+
+  <h2>
+    <a id="instance-method-summary" class="anchor" href="#instance-method-summary">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Instance Method Summary
+  </h2>
+  <ul class="list-summary">
+    
+      <li class="entry-summary">
+        <a href="#pdf(x)-instance-method" class="signature"><strong>#pdf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Density Function (PDF) of a continuous random variable.</p></div>
+        
+      </li>
+    
+  </ul>
+
+
+
+
+
+<div class="methods-inherited">
+  
+    
+
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/Distribution.html#rand:T-instance-method" class="tooltip">
+      <span>rand : T</span>
+    rand</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
+
+    
+
+
+    
+
+
+  
+    
+
+
+    
+
+
+    
+
+
+  
+</div>
+
+
+
+
+
+
+  <h2>
+    <a id="instance-method-detail" class="anchor" href="#instance-method-detail">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Instance Method Detail
+  </h2>
+  
+    <div class="entry-detail" id="pdf(x)-instance-method">
+      <div class="signature">
+        abstract 
+        def <strong>pdf</strong>(x)
+
+        <a class="method-permalink" href="#pdf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+          <p>The Probability Density Function (PDF) of a continuous
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L17" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+
+
+
+
+</div>
+
+</body>
+</html>
diff --git a/docs/Statistics/Distributions/DiscreteDistribution.html b/docs/Statistics/Distributions/DiscreteDistribution.html
new file mode 100644
index 0000000..3125c3b
--- /dev/null
+++ b/docs/Statistics/Distributions/DiscreteDistribution.html
@@ -0,0 +1,292 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="utf-8" />
+<meta http-equiv="X-UA-Compatible" content="IE=edge">
+<meta name="generator" content="Crystal Docs 0.33.0">
+
+<link href="../../css/style.css" rel="stylesheet" type="text/css" />
+<script type="text/javascript" src="../../js/doc.js"></script>
+
+<svg class="hidden">
+  <symbol id="octicon-link" viewBox="0 0 16 16">
+    <path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path>
+  </symbol>
+</svg>
+
+  <meta id="repository-name" content="github.com/lbarasti/statistics">
+  <title>Statistics::Distributions::DiscreteDistribution(T) - github.com/lbarasti/statistics</title>
+  <script type="text/javascript">
+    CrystalDoc.base_path = "../../";
+  </script>
+</head>
+<body>
+
+<div class="sidebar">
+  <div class="sidebar-header">
+    <div class="search-box">
+      <input type="search" class="search-input" placeholder="Search..." spellcheck="false" aria-label="Search">
+    </div>
+
+    <div class="repository-links">
+      <a href="../../index.html">README</a>
+    </div>
+  </div>
+
+  <div class="search-results" class="hidden">
+    <ul class="search-list"></ul>
+  </div>
+
+  <div class="types-list">
+    <ul>
+  
+  <li class="parent open current" data-id="github.com/lbarasti/statistics/Statistics" data-name="statistics">
+      <a href="../../Statistics.html">Statistics</a>
+      
+        <ul>
+  
+  <li class="parent open current" data-id="github.com/lbarasti/statistics/Statistics/Distributions" data-name="statistics::distributions">
+      <a href="../../Statistics/Distributions.html">Distributions</a>
+      
+        <ul>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
+      <a href="../../Statistics/Distributions/Constant.html">Constant</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" current" data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
+      <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Exponential" data-name="statistics::distributions::exponential">
+      <a href="../../Statistics/Distributions/Exponential.html">Exponential</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Normal" data-name="statistics::distributions::normal">
+      <a href="../../Statistics/Distributions/Normal.html">Normal</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Poisson" data-name="statistics::distributions::poisson">
+      <a href="../../Statistics/Distributions/Poisson.html">Poisson</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Uniform" data-name="statistics::distributions::uniform">
+      <a href="../../Statistics/Distributions/Uniform.html">Uniform</a>
+      
+    </li>
+  
+</ul>
+
+      
+    </li>
+  
+</ul>
+
+      
+    </li>
+  
+</ul>
+
+  </div>
+</div>
+
+
+<div class="main-content">
+<h1 class="type-name">
+
+  <span class="kind">abstract class</span> Statistics::Distributions::DiscreteDistribution(T)
+
+</h1>
+
+
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(T)</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(T)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+
+
+
+
+
+
+
+
+
+
+
+
+  <h2>
+    <a id="direct-known-subclasses" class="anchor" href="#direct-known-subclasses">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Direct Known Subclasses
+  </h2>
+  <ul class="other-types-list">
+    
+      <li class="other-type"><a href="../../Statistics/Distributions/Bernoulli.html">Statistics::Distributions::Bernoulli</a></li>
+    
+      <li class="other-type"><a href="../../Statistics/Distributions/Constant.html">Statistics::Distributions::Constant</a></li>
+    
+      <li class="other-type"><a href="../../Statistics/Distributions/Poisson.html">Statistics::Distributions::Poisson</a></li>
+    
+  </ul>
+
+
+
+
+
+
+  <h2>
+    <a id="defined-in" class="anchor" href="#defined-in">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Defined in:
+  </h2>
+  
+    
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L8" target="_blank">
+        lib/distributions.cr
+      </a>
+    
+    <br/>
+  
+
+
+
+
+
+
+
+
+
+  <h2>
+    <a id="instance-method-summary" class="anchor" href="#instance-method-summary">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Instance Method Summary
+  </h2>
+  <ul class="list-summary">
+    
+      <li class="entry-summary">
+        <a href="#pmf(x)-instance-method" class="signature"><strong>#pmf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Mass Function (PMF) of a discrete random variable.</p></div>
+        
+      </li>
+    
+  </ul>
+
+
+
+
+
+<div class="methods-inherited">
+  
+    
+
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(T)</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/Distribution.html#rand:T-instance-method" class="tooltip">
+      <span>rand : T</span>
+    rand</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
+
+    
+
+
+    
+
+
+  
+    
+
+
+    
+
+
+    
+
+
+  
+</div>
+
+
+
+
+
+
+  <h2>
+    <a id="instance-method-detail" class="anchor" href="#instance-method-detail">
+  <svg class="octicon-link" aria-hidden="true">
+    <use href="#octicon-link"/>
+  </svg>
+</a>
+    Instance Method Detail
+  </h2>
+  
+    <div class="entry-detail" id="pmf(x)-instance-method">
+      <div class="signature">
+        abstract 
+        def <strong>pmf</strong>(x)
+
+        <a class="method-permalink" href="#pmf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+          <p>The Probability Mass Function (PMF) of a discrete
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L11" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+
+
+
+
+</div>
+
+</body>
+</html>
diff --git a/docs/Statistics/Distributions/Distribution.html b/docs/Statistics/Distributions/Distribution.html
index abc0978..77e59eb 100644
--- a/docs/Statistics/Distributions/Distribution.html
+++ b/docs/Statistics/Distributions/Distribution.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="../../Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" current" data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -127,15 +142,9 @@ <h2>
   </h2>
   <ul class="other-types-list">
     
-      <li class="other-type"><a href="../../Statistics/Distributions/Constant.html">Statistics::Distributions::Constant</a></li>
-    
-      <li class="other-type"><a href="../../Statistics/Distributions/Exponential.html">Statistics::Distributions::Exponential</a></li>
-    
-      <li class="other-type"><a href="../../Statistics/Distributions/Normal.html">Statistics::Distributions::Normal</a></li>
-    
-      <li class="other-type"><a href="../../Statistics/Distributions/Poisson.html">Statistics::Distributions::Poisson</a></li>
+      <li class="other-type"><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></li>
     
-      <li class="other-type"><a href="../../Statistics/Distributions/Uniform.html">Statistics::Distributions::Uniform</a></li>
+      <li class="other-type"><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(T)</a></li>
     
   </ul>
 
@@ -154,7 +163,7 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L3" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L3" target="_blank">
         lib/distributions.cr
       </a>
     
@@ -246,7 +255,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L5" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L5" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Statistics/Distributions/Exponential.html b/docs/Statistics/Distributions/Exponential.html
index 2267282..c535145 100644
--- a/docs/Statistics/Distributions/Exponential.html
+++ b/docs/Statistics/Distributions/Exponential.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="../../Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -104,7 +119,7 @@ <h1 class="type-name">
 </h1>
 
 
-  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Exponential.html">Statistics::Distributions::Exponential</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Exponential.html">Statistics::Distributions::Exponential</a></li><li class="superclass"><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
 
 
 
@@ -147,7 +162,7 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L22" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L59" target="_blank">
         lib/distributions.cr
       </a>
     
@@ -191,6 +206,13 @@ <h2>
   </h2>
   <ul class="list-summary">
     
+      <li class="entry-summary">
+        <a href="#pdf(x)-instance-method" class="signature"><strong>#pdf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Density Function (PDF) of a continuous random variable.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#rand:Float64-instance-method" class="signature"><strong>#rand</strong> : Float64</a>
         
@@ -208,6 +230,25 @@ <h2>
   
     
 
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/ContinuousDistribution.html#pdf(x)-instance-method" class="tooltip">
+      <span>pdf(x)</span>
+    pdf</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
   <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></code></h3>
   
   
@@ -273,7 +314,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L24" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L61" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -292,6 +333,32 @@ <h2>
     Instance Method Detail
   </h2>
   
+    <div class="entry-detail" id="pdf(x)-instance-method">
+      <div class="signature">
+        
+        def <strong>pdf</strong>(x)
+
+        <a class="method-permalink" href="#pdf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+            <div class="doc-inherited">
+              Description copied from class <a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a>
+            </div>
+          
+          <p>The Probability Density Function (PDF) of a continuous
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L64" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
     <div class="entry-detail" id="rand:Float64-instance-method">
       <div class="signature">
         
@@ -312,7 +379,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L27" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L70" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Statistics/Distributions/Normal.html b/docs/Statistics/Distributions/Normal.html
index dd23130..37f1df8 100644
--- a/docs/Statistics/Distributions/Normal.html
+++ b/docs/Statistics/Distributions/Normal.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="../../Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -104,7 +119,7 @@ <h1 class="type-name">
 </h1>
 
 
-  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Normal.html">Statistics::Distributions::Normal</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Normal.html">Statistics::Distributions::Normal</a></li><li class="superclass"><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
 
 
 
@@ -145,7 +160,7 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L38" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L81" target="_blank">
         lib/distributions.cr
       </a>
     
@@ -166,6 +181,11 @@ <h2>
   
   <dl>
     
+      <dt class="entry-const" id="PDF_COEFFICIENT">
+        <strong>PDF_COEFFICIENT</strong> = <code><span class="n">1</span> <span class="o">/</span> (<span class="t">Math</span>.sqrt(<span class="t">TWO_PI</span>))</code>
+      </dt>
+      
+    
       <dt class="entry-const" id="TWO_PI">
         <strong>TWO_PI</strong> = <code><span class="n">2</span> <span class="o">*</span> <span class="t">Math</span><span class="t">::</span><span class="t">PI</span></code>
       </dt>
@@ -186,7 +206,7 @@ <h2>
   <ul class="list-summary">
     
       <li class="entry-summary">
-        <a href="#new(mean:Float64,std:Float64)-class-method" class="signature"><strong>.new</strong>(mean : Float64, std : Float64)</a>
+        <a href="#new(mean:Float64=0,std:Float64=1)-class-method" class="signature"><strong>.new</strong>(mean : Float64 = <span class="n">0</span>, std : Float64 = <span class="n">1</span>)</a>
         
           <div class="summary"><p>Creates a normal distribution with the given <code>mean</code> and <code>std</code>.</p></div>
         
@@ -208,6 +228,13 @@ <h2>
   </h2>
   <ul class="list-summary">
     
+      <li class="entry-summary">
+        <a href="#pdf(x)-instance-method" class="signature"><strong>#pdf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Density Function (PDF) of a continuous random variable.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#rand:Float64-instance-method" class="signature"><strong>#rand</strong> : Float64</a>
         
@@ -225,6 +252,25 @@ <h2>
   
     
 
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/ContinuousDistribution.html#pdf(x)-instance-method" class="tooltip">
+      <span>pdf(x)</span>
+    pdf</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
   <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></code></h3>
   
   
@@ -274,12 +320,12 @@ <h2>
     Constructor Detail
   </h2>
   
-    <div class="entry-detail" id="new(mean:Float64,std:Float64)-class-method">
+    <div class="entry-detail" id="new(mean:Float64=0,std:Float64=1)-class-method">
       <div class="signature">
         
-        def self.<strong>new</strong>(mean : Float64, std : Float64)
+        def self.<strong>new</strong>(mean : Float64 = <span class="n">0</span>, std : Float64 = <span class="n">1</span>)
 
-        <a class="method-permalink" href="#new(mean:Float64,std:Float64)-class-method">#</a>
+        <a class="method-permalink" href="#new(mean:Float64=0,std:Float64=1)-class-method">#</a>
       </div>
       
         <div class="doc">
@@ -290,7 +336,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L42" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L86" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -309,6 +355,32 @@ <h2>
     Instance Method Detail
   </h2>
   
+    <div class="entry-detail" id="pdf(x)-instance-method">
+      <div class="signature">
+        
+        def <strong>pdf</strong>(x)
+
+        <a class="method-permalink" href="#pdf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+            <div class="doc-inherited">
+              Description copied from class <a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a>
+            </div>
+          
+          <p>The Probability Density Function (PDF) of a continuous
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L89" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
     <div class="entry-detail" id="rand:Float64-instance-method">
       <div class="signature">
         
@@ -329,7 +401,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L45" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L94" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Statistics/Distributions/Poisson.html b/docs/Statistics/Distributions/Poisson.html
index 4a5e920..b31e81c 100644
--- a/docs/Statistics/Distributions/Poisson.html
+++ b/docs/Statistics/Distributions/Poisson.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="../../Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -104,7 +119,7 @@ <h1 class="type-name">
 </h1>
 
 
-  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Poisson.html">Statistics::Distributions::Poisson</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Int32)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Poisson.html">Statistics::Distributions::Poisson</a></li><li class="superclass"><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Int32)</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Int32)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
 
 
 
@@ -147,7 +162,7 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L58" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L107" target="_blank">
         lib/distributions.cr
       </a>
     
@@ -191,6 +206,13 @@ <h2>
   </h2>
   <ul class="list-summary">
     
+      <li class="entry-summary">
+        <a href="#pmf(x)-instance-method" class="signature"><strong>#pmf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Mass Function (PMF) of a discrete random variable.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#rand:Int32-instance-method" class="signature"><strong>#rand</strong> : Int32</a>
         
@@ -208,6 +230,25 @@ <h2>
   
     
 
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Int32)</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/DiscreteDistribution.html#pmf(x)-instance-method" class="tooltip">
+      <span>pmf(x)</span>
+    pmf</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
   <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Int32)</a></code></h3>
   
   
@@ -273,7 +314,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L60" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L109" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -292,6 +333,32 @@ <h2>
     Instance Method Detail
   </h2>
   
+    <div class="entry-detail" id="pmf(x)-instance-method">
+      <div class="signature">
+        
+        def <strong>pmf</strong>(x)
+
+        <a class="method-permalink" href="#pmf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+            <div class="doc-inherited">
+              Description copied from class <a href="../../Statistics/Distributions/DiscreteDistribution.html">Statistics::Distributions::DiscreteDistribution(Int32)</a>
+            </div>
+          
+          <p>The Probability Mass Function (PMF) of a discrete
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L112" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
     <div class="entry-detail" id="rand:Int32-instance-method">
       <div class="signature">
         
@@ -312,7 +379,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L63" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L122" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Statistics/Distributions/Uniform.html b/docs/Statistics/Distributions/Uniform.html
index 960f308..853fc51 100644
--- a/docs/Statistics/Distributions/Uniform.html
+++ b/docs/Statistics/Distributions/Uniform.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="../../Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="../../Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="../../Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="../../Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="../../Statistics/Distributions/Distribution.html">Distribution</a>
       
@@ -104,7 +119,7 @@ <h1 class="type-name">
 </h1>
 
 
-  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Uniform.html">Statistics::Distributions::Uniform</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
+  <ul class="superclass-hierarchy"><li class="superclass"><a href="../../Statistics/Distributions/Uniform.html">Statistics::Distributions::Uniform</a></li><li class="superclass"><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></li><li class="superclass"><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
 
 
 
@@ -145,7 +160,7 @@ <h2>
   </h2>
   
     
-      <a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L84" target="_blank">
+      <a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L143" target="_blank">
         lib/distributions.cr
       </a>
     
@@ -189,6 +204,13 @@ <h2>
   </h2>
   <ul class="list-summary">
     
+      <li class="entry-summary">
+        <a href="#pdf(x)-instance-method" class="signature"><strong>#pdf</strong>(x)</a>
+        
+          <div class="summary"><p>The Probability Density Function (PDF) of a continuous random variable.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#rand:Float64-instance-method" class="signature"><strong>#rand</strong> : Float64</a>
         
@@ -206,6 +228,25 @@ <h2>
   
     
 
+  <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a></code></h3>
+  
+  
+    <a href="../../Statistics/Distributions/ContinuousDistribution.html#pdf(x)-instance-method" class="tooltip">
+      <span>pdf(x)</span>
+    pdf</a>
+    
+  
+
+
+    
+
+
+    
+
+
+  
+    
+
   <h3>Instance methods inherited from class <code><a href="../../Statistics/Distributions/Distribution.html">Statistics::Distributions::Distribution(Float64)</a></code></h3>
   
   
@@ -271,7 +312,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L88" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L147" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -290,6 +331,32 @@ <h2>
     Instance Method Detail
   </h2>
   
+    <div class="entry-detail" id="pdf(x)-instance-method">
+      <div class="signature">
+        
+        def <strong>pdf</strong>(x)
+
+        <a class="method-permalink" href="#pdf(x)-instance-method">#</a>
+      </div>
+      
+        <div class="doc">
+          
+            <div class="doc-inherited">
+              Description copied from class <a href="../../Statistics/Distributions/ContinuousDistribution.html">Statistics::Distributions::ContinuousDistribution</a>
+            </div>
+          
+          <p>The Probability Density Function (PDF) of a continuous
+random variable.</p>
+        </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L151" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
     <div class="entry-detail" id="rand:Float64-instance-method">
       <div class="signature">
         
@@ -310,7 +377,7 @@ <h2>
       <br/>
       <div>
         
-          [<a href="https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr#L92" target="_blank">View source</a>]
+          [<a href="https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr#L159" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/index.html b/docs/index.html
index 7c7a895..edb6ce9 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -50,11 +50,26 @@
       
         <ul>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Bernoulli" data-name="statistics::distributions::bernoulli">
+      <a href="Statistics/Distributions/Bernoulli.html">Bernoulli</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Constant" data-name="statistics::distributions::constant">
       <a href="Statistics/Distributions/Constant.html">Constant</a>
       
     </li>
   
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution" data-name="statistics::distributions::continuousdistribution">
+      <a href="Statistics/Distributions/ContinuousDistribution.html">ContinuousDistribution</a>
+      
+    </li>
+  
+  <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution" data-name="statistics::distributions::discretedistribution(t)">
+      <a href="Statistics/Distributions/DiscreteDistribution.html">DiscreteDistribution</a>
+      
+    </li>
+  
   <li class=" " data-id="github.com/lbarasti/statistics/Statistics/Distributions/Distribution" data-name="statistics::distributions::distribution(t)">
       <a href="Statistics/Distributions/Distribution.html">Distribution</a>
       
diff --git a/docs/index.json b/docs/index.json
index a570e56..c9014e8 100644
--- a/docs/index.json
+++ b/docs/index.json
@@ -1 +1 @@
-{"repository_name":"github.com/lbarasti/statistics","body":"[![GitHub release](https://img.shields.io/github/release/lbarasti/statistics.svg)](https://github.com/lbarasti/statistics/releases)\n![Build Status](https://github.com/lbarasti/statistics/workflows/build/badge.svg)\n[![License](https://img.shields.io/badge/license-MIT-blue.svg)](https://opensource.org/licenses/MIT)\n\n# statistics\n\nA statistical library to perform descriptive statistics and generate random values based on popular probability distributions.\n\n## Installation\n\n1. Add the dependency to your `shard.yml`:\n\n```yaml\ndependencies:\n  statistics:\n    github: lbarasti/statistics\n```\n\n2. Run `shards install`\n\n## Usage\n\n```crystal\nrequire \"statistics\"\n```\n\n### Descriptive statistics\nYou can compute mean, variance and standard deviation of a collection as follows.\n```crystal\ninclude Statistics\n\nx = [1, 10, 7]\nmean(x) # 6\nvar(x) # 14\nstd(x) # 3.7416...\n```\n\nIf you'd like to know a bit more about your dataset, you can simply `describe` it\n\n```crystal\nx = (1..1000).map { rand }.to_a # a uniformely distributed dataset\ndescribe(x)\n# {\n#   mean: 0.48, var: 0.08, std: 0.28, \n#   skewness: 0.04, kurtosis: 1.81, \n#   min: 0.01, middle: 0.49, max: 0.99, \n#   q1: 0.24, median: 0.49, q3: 0.73\n# }\n```\n\n`Statistics.describe` returns a `NamedTuple`, so you can extract any value via indexing:\n\n```crystal\nstats = describe(x)\nstats[:q1] # returns the first quartile of your sample\n```\n\nFor a complete list of the statistical functions provided, including `quantile`, `moment` and `skew`, check out the [docs](https://lbarasti.com/statistics/Statistics.html).\n\n### Sampling\nTo work with distributions, import the `Distributions` namespace as follows.\n```crystal\ninclude Statistics::Distributions\n```\n\nNow, here is how we sample values from a normal distribution with `mean = 1.5` and `std = 0.2`.\n```crystal\nNormal.new(1.5, 0.2).rand\n```\n\nWe can generate an iterable of normally distributed random values as follows.\n```crystal\ngen = Normal.new(1.5, 0.2)\n1000.times.map { gen.rand }\n```\n\n#### Supported distributions\nThe following distributions are supported:\n* Constant\n* Exponential\n* Normal\n* Poisson\n* Uniform\n\nDon't see your favourite one on the list? Just fork the repo, add your distribution to the `distributions.cr` file, and open a PR.\n\n## Development\n\nThis shard is a work in progress. Everyone's contribution is welcome.\n\nThe guiding principle at this stage is\n> make it work before you make it right\n\nWhich in this context means: let's not focus on benchmarks and performance, but rather on usability and correctness.\n\n## References\n* [numpy.random](https://numpy.org/devdocs/reference/random/generator.html): distributions and random sampling\n* [numpy statistics](https://numpy.org/devdocs/reference/routines.statistics.html#averages-and-variances): order statistics, averages and variances\n* [scipy stats](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py) module and related [tests](https://github.com/scipy/scipy/blob/1150c4c033899a5a4556b7d34d6b137352b36b9e/scipy/stats/tests/test_stats.py) tests\n* [julia random](https://docs.julialang.org/en/v1/stdlib/Random/) module\n* [julia statistics](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.std) module\n* [julia distributions](https://juliastats.org/Distributions.jl/latest/starting/) package.\n* on [skewness and kurtosis](https://brownmath.com/stat/shape.htm), by Stan Brown\n* more on [skewness and kurtosis](https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm), from NIST.\n\n## Contributing\n\n1. Fork it (<https://github.com/lbarasti/statistics/fork>)\n2. Create your feature branch (`git checkout -b my-new-feature`)\n3. Commit your changes (`git commit -am 'Add some feature'`)\n4. Push to the branch (`git push origin my-new-feature`)\n5. Create a new Pull Request\n\n## Contributors\n\n- [lbarasti](https://github.com/lbarasti) - creator and maintainer\n","program":{"html_id":"github.com/lbarasti/statistics/toplevel","path":"toplevel.html","kind":"module","full_name":"Top Level Namespace","name":"Top Level Namespace","abstract":false,"superclass":null,"ancestors":[],"locations":[],"repository_name":"github.com/lbarasti/statistics","program":true,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":null,"doc":null,"summary":null,"class_methods":[],"constructors":[],"instance_methods":[],"macros":[],"types":[{"html_id":"github.com/lbarasti/statistics/Statistics","path":"Statistics.html","kind":"module","full_name":"Statistics","name":"Statistics","abstract":false,"superclass":null,"ancestors":[],"locations":[{"filename":"lib/distributions.cr","line_number":1,"url":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr"},{"filename":"statistics.cr","line_number":6,"url":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[{"id":"VERSION","name":"VERSION","value":"\"0.3.0\"","doc":null,"summary":null}],"included_modules":[],"extended_modules":[{"html_id":"github.com/lbarasti/statistics/Statistics","kind":"module","full_name":"Statistics","name":"Statistics"}],"subclasses":[],"including_types":[],"namespace":null,"doc":"Basic descriptive statistics functionality.\n\nMore flexible than a scientific-calculator, but not as exhaustive, yet.","summary":"<p>Basic descriptive statistics functionality.</p>","class_methods":[],"constructors":[],"instance_methods":[{"id":"bin_count(values:Enumerable,bins:Int32,min=nil,max=nil):Array(::Tuple(Float64,Int32))-instance-method","html_id":"bin_count(values:Enumerable,bins:Int32,min=nil,max=nil):Array(::Tuple(Float64,Int32))-instance-method","name":"bin_count","doc":"Counts the number of values in each bin of size `(max - min) / bins`.\n\nReturns an array of tuples `{edge, count}` ordered by `edge`, where `edge` is the\nstarting edge of a bin and `count` is the number of values in the corresponding `bin`.\n\nNOTE: Any empty bin will also be included.\n\nParameters\n- values: a one-dimensional dataset.\n- bins: the number of equally-sized bins to divide the datapoints into.\n- min: the left end of the first bin's edge. If none is provided, then `values.min` is used.\n- max: the right end of the last bin's edge. If none is provided, then `values.max` is used.","summary":"<p>Counts the number of values in each bin of size <code>(max - min) / bins</code>.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"},{"name":"bins","doc":null,"default_value":"","external_name":"bins","restriction":"Int32"},{"name":"min","doc":null,"default_value":"nil","external_name":"min","restriction":""},{"name":"max","doc":null,"default_value":"nil","external_name":"max","restriction":""}],"args_string":"(values : Enumerable, bins : Int32, min = <span class=\"n\">nil</span>, max = <span class=\"n\">nil</span>) : Array(::Tuple(Float64, Int32))","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L57","def":{"name":"bin_count","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"},{"name":"bins","doc":null,"default_value":"","external_name":"bins","restriction":"Int32"},{"name":"min","doc":null,"default_value":"nil","external_name":"min","restriction":""},{"name":"max","doc":null,"default_value":"nil","external_name":"max","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Array(::Tuple(Float64, Int32))","visibility":"Public","body":"if min.nil? || max.nil?\n  sample_min, sample_max = values.minmax\n  if min.nil?\n    min = sample_min\n  end\n  if max.nil?\n    max = sample_max\n  end\nend\ncounter = Array(Int32).new(size: bins, value: 0)\nstep = (max - min) / bins\nvalues.each do |v|\n  idx = v == max ? bins - 1 : ((v - min) / step).floor.to_i\n  __temp_26 = idx\n  counter[__temp_26] = counter[__temp_26] + 1\nend\nArray.new(bins) do |i|\n  {min + (i * step), counter[i]}\nend\n"}},{"id":"describe(values)-instance-method","html_id":"describe(values)-instance-method","name":"describe","doc":"Computes several descriptive statistics of the passed array.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes several descriptive statistics of the passed array.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L14","def":{"name":"describe","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nsorted = values.sort\n{mean: mean(values), var: var(values), std: std(values), skewness: skew(values), kurtosis: kurtosis(values), min: sorted.first, middle: middle(sorted), max: sorted.last, q1: quantile(sorted, 0.25, sorted: true), median: median(sorted, sorted: true), q3: quantile(sorted, 0.75, sorted: true)}\n"}},{"id":"frequency(values:Enumerable(T))forallT-instance-method","html_id":"frequency(values:Enumerable(T))forallT-instance-method","name":"frequency","doc":"Computes the number of occurrences of each value in the dataset.\n\nReturns a Hash with each the dataset values as keys and the number of times they appear as value.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the number of occurrences of each value in the dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable(T)"}],"args_string":"(values : Enumerable(T)) forall T","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L38","def":{"name":"frequency","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable(T)"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"values.reduce(Hash(T, Int32).new(0)) do |freq, v|\n  __temp_24 = v\n  freq[__temp_24] = freq[__temp_24] + 1\n  freq\nend"}},{"id":"kurtosis(values,corrected=false,excess=false)-instance-method","html_id":"kurtosis(values,corrected=false,excess=false)-instance-method","name":"kurtosis","doc":"Computes the kurtosis of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- corrected: when set to `true`, then the calculations are corrected for statistical bias. Default is `false`.\n- excess: when set to `true`, computes the [excess kurtosis](https://en.wikipedia.org/wiki/Kurtosis#Excess_kurtosis). Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1142).","summary":"<p>Computes the kurtosis of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>, excess = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L84","def":{"name":"kurtosis","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm4 = moment(values, m, 4)\nm2 = moment(values, m, 2)\nkurt = if corrected\n  (((1 / (n - 2)) / (n - 3)) * (((((n ** 2) - 1) * m4) / (m2 ** 2)) - (3 * ((n - 1) ** 2)))) + 3\nelse\n  m4 / (m2 ** 2)\nend\nexcess ? kurt - 3 : kurt\n"}},{"id":"mean(values)-instance-method","html_id":"mean(values)-instance-method","name":"mean","doc":"Computes the mean of a dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the mean of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L103","def":{"name":"mean","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(values.reduce(0) do |acc, v|\n  acc + v\nend) / values.size"}},{"id":"median(values,sorted=false)-instance-method","html_id":"median(values,sorted=false)-instance-method","name":"median","doc":"Computes the median of all elements in a dataset.\n\nFor an even number of elements the mean of the two median elements will be computed.\n\nParameters\n- values: a one-dimensional dataset.\n- sorted: when `true`, the computations assume that the provided values are\n  sorted. Default is `false`.\n\nSee Julia's [Statistics.median](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.median).","summary":"<p>Computes the median of all elements in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L117","def":{"name":"median","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nmid = size // 2\nsorted_values = sorted ? values : values.sort\nif size.odd?\n  sorted_values[mid]\nelse\n  middle([sorted_values[mid - 1], sorted_values[mid]])\nend\n"}},{"id":"middle(a,b)-instance-method","html_id":"middle(a,b)-instance-method","name":"middle","doc":"Computes the middle of two values `a` and `b`.","summary":"<p>Computes the middle of two values <code>a</code> and <code>b</code>.</p>","abstract":false,"args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"args_string":"(a, b)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L142","def":{"name":"middle","args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"0.5 * (a + b)"}},{"id":"middle(values)-instance-method","html_id":"middle(values)-instance-method","name":"middle","doc":"Computes the middle of an array `a`, which consists of finding its\nextrema and then computing their mean.\n\nParameters\n- values: a one-dimensional dataset.\n\nSee Julia's [Statistics.middle](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.middle).","summary":"<p>Computes the middle of an array <code>a</code>, which consists of finding its extrema and then computing their mean.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L136","def":{"name":"middle","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min, max = values.minmax\nmiddle(min, max)\n"}},{"id":"mode(values:Enumerable)-instance-method","html_id":"mode(values:Enumerable)-instance-method","name":"mode","doc":"Computes the modal (most common) value in a dataset.\n\nReturns a pair with the modal value and the bin-count for the modal bin.\nIf there is more than one such value, no guarantees are made which one will be picked.\nNOTE: Computing the mode requires traversing the entire dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the modal (most common) value in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"args_string":"(values : Enumerable)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L154","def":{"name":"mode","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(frequency(values)).max_by(&.last)"}},{"id":"moment(values,mean=nil,n=1)-instance-method","html_id":"moment(values,mean=nil,n=1)-instance-method","name":"moment","doc":"Calculates the n-th moment about the mean for a sample.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- n: order of central moment that is returned. Default is `1`.","summary":"<p>Calculates the n-th moment about the mean for a sample.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, n = <span class=\"n\">1</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L165","def":{"name":"moment","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"m = mean || (Statistics.mean(values))\n(values.reduce(0) do |a, b|\n  a + ((b - m) ** n)\nend) / values.size\n"}},{"id":"quantile(values,p,sorted=false)-instance-method","html_id":"quantile(values,p,sorted=false)-instance-method","name":"quantile","doc":"Computes the quantile of a dataset at a specified probability `p` on the interval [0,1].\n\nQuantiles are computed via linear interpolation between the points `((k-1)/(n-1), v[k])`,\nfor `k = 1:n` where `n = values.size`.\n\nParameters\n- values: a one-dimensional dataset.\n- p: probability. Values of `p` should be in the interval `[0, 1]`.\n- sorted indicates whether values can be assumed to be sorted.\n\nImplementation based on Julia's [Statistics.quantile](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.quantile).","summary":"<p>Computes the quantile of a dataset at a specified probability <code>p</code> on the interval [0,1].</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, p, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L181","def":{"name":"quantile","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sorted_values = sorted ? values : values.sort\nn = values.size\naleph = (n - 1) * p\nj = (clamp(aleph.floor, 0, n - 2)).to_i\ngamma = clamp(aleph - j, 0, 1)\na = sorted_values[j]\nb = sorted_values[j + 1]\na + ((b - a) * gamma)\n"}},{"id":"skew(values,corrected=false)-instance-method","html_id":"skew(values,corrected=false)-instance-method","name":"skew","doc":"Computes the skewness of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- corrected: when set to `true`, then the calculations are corrected for statistical bias. Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1039).","summary":"<p>Computes the skewness of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L201","def":{"name":"skew","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm3 = moment(values, m, 3)\nm2 = moment(values, m, 2)\ncorrection_factor = corrected ? (Math.sqrt((n - 1.0) * n)) / (n - 2.0) : 1\n(correction_factor * m3) / (m2 ** 1.5)\n"}},{"id":"std(values,mean=nil,corrected=false)-instance-method","html_id":"std(values,mean=nil,corrected=false)-instance-method","name":"std","doc":"Computes the standard deviation of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. Default is `false`.","summary":"<p>Computes the standard deviation of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L219","def":{"name":"std","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Math.sqrt(var(values, mean, corrected))"}},{"id":"var(values,mean=nil,corrected=false)-instance-method","html_id":"var(values,mean=nil,corrected=false)-instance-method","name":"var","doc":"Computes the variance of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. Default is `false`.","summary":"<p>Computes the variance of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L232","def":{"name":"var","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"correction_factor = corrected ? values.size / (values.size - 1) : 1\n(moment(values, mean, 2)) * correction_factor\n"}}],"macros":[],"types":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions","path":"Statistics/Distributions.html","kind":"module","full_name":"Statistics::Distributions","name":"Distributions","abstract":false,"superclass":null,"ancestors":[],"locations":[{"filename":"lib/distributions.cr","line_number":2,"url":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":{"html_id":"github.com/lbarasti/statistics/Statistics","kind":"module","full_name":"Statistics","name":"Statistics"},"doc":null,"summary":null,"class_methods":[],"constructors":[],"instance_methods":[],"macros":[],"types":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Constant","path":"Statistics/Distributions/Constant.html","kind":"class","full_name":"Statistics::Distributions::Constant","name":"Constant","abstract":false,"superclass":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Distribution","kind":"class","full_name":"Statistics::Distributions::Distribution","name":"Distribution"},"ancestors":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Distribution","kind":"class","full_name":"Statistics::Distributions::Distribution","name":"Distribution"},{"html_id":"github.com/lbarasti/statistics/Reference","kind":"class","full_name":"Reference","name":"Reference"},{"html_id":"github.com/lbarasti/statistics/Object","kind":"class","full_name":"Object","name":"Object"}],"locations":[{"filename":"lib/distributions.cr","line_number":9,"url":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions","kind":"module","full_name":"Statistics::Distributions","name":"Distributions"},"doc":"Represents 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+{"repository_name":"github.com/lbarasti/statistics","body":"[![GitHub release](https://img.shields.io/github/release/lbarasti/statistics.svg)](https://github.com/lbarasti/statistics/releases)\n![Build Status](https://github.com/lbarasti/statistics/workflows/build/badge.svg)\n[![License](https://img.shields.io/badge/license-MIT-blue.svg)](https://opensource.org/licenses/MIT)\n\n# statistics\n\nA statistical library to perform descriptive statistics and generate random values based on popular probability distributions.\n\n## Installation\n\n1. Add the dependency to your `shard.yml`:\n\n```yaml\ndependencies:\n  statistics:\n    github: lbarasti/statistics\n```\n\n2. Run `shards install`\n\n## Usage\n\n```crystal\nrequire \"statistics\"\n```\n\n### Descriptive statistics\nYou can compute mean, variance and standard deviation of a collection as follows.\n```crystal\ninclude Statistics\n\nx = [1, 10, 7]\nmean(x) # 6\nvar(x) # 14\nstd(x) # 3.7416...\n```\n\nIf you'd like to know a bit more about your dataset, you can simply `describe` it\n\n```crystal\nx = (1..1000).map { rand }.to_a # a uniformely distributed dataset\ndescribe(x)\n# {\n#   mean: 0.48, var: 0.08, std: 0.28, \n#   skewness: 0.04, kurtosis: 1.81, \n#   min: 0.01, middle: 0.49, max: 0.99, \n#   q1: 0.24, median: 0.49, q3: 0.73\n# }\n```\n\n`Statistics.describe` returns a `NamedTuple`, so you can extract any value via indexing:\n\n```crystal\nstats = describe(x)\nstats[:q1] # returns the first quartile of your sample\n```\n\nFor a complete list of the statistical functions provided, including `quantile`, `moment` and `skew`, check out the [docs](https://lbarasti.com/statistics/Statistics.html).\n\n### Sampling\nTo work with distributions, import the `Distributions` namespace as follows.\n```crystal\ninclude Statistics::Distributions\n```\n\nNow, here is how we sample values from a normal distribution with `mean = 1.5` and `std = 0.2`.\n```crystal\nNormal.new(1.5, 0.2).rand\n```\n\nWe can generate an iterable of normally distributed random values as follows.\n```crystal\ngen = Normal.new(1.5, 0.2)\n1000.times.map { gen.rand }\n```\n\n#### Supported distributions\nThe following distributions are supported:\n* Constant\n* Exponential\n* Normal\n* Poisson\n* Uniform\n\nDon't see your favourite one on the list? Just fork the repo, add your distribution to the `distributions.cr` file, and open a PR.\n\n## Development\n\nThis shard is a work in progress. Everyone's contribution is welcome.\n\nThe guiding principle at this stage is\n> make it work before you make it right\n\nWhich in this context means: let's not focus on benchmarks and performance, but rather on usability and correctness.\n\n## References\n* [numpy.random](https://numpy.org/devdocs/reference/random/generator.html): distributions and random sampling\n* [numpy statistics](https://numpy.org/devdocs/reference/routines.statistics.html#averages-and-variances): order statistics, averages and variances\n* [scipy stats](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py) module and related [tests](https://github.com/scipy/scipy/blob/1150c4c033899a5a4556b7d34d6b137352b36b9e/scipy/stats/tests/test_stats.py) tests\n* [julia random](https://docs.julialang.org/en/v1/stdlib/Random/) module\n* [julia statistics](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.std) module\n* [julia distributions](https://juliastats.org/Distributions.jl/latest/starting/) package.\n* on [skewness and kurtosis](https://brownmath.com/stat/shape.htm), by Stan Brown\n* more on [skewness and kurtosis](https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm), from NIST.\n\n## Contributing\n\n1. Fork it (<https://github.com/lbarasti/statistics/fork>)\n2. Create your feature branch (`git checkout -b my-new-feature`)\n3. Commit your changes (`git commit -am 'Add some feature'`)\n4. Push to the branch (`git push origin my-new-feature`)\n5. Create a new Pull Request\n\n## Contributors\n\n- [lbarasti](https://github.com/lbarasti) - creator and maintainer\n","program":{"html_id":"github.com/lbarasti/statistics/toplevel","path":"toplevel.html","kind":"module","full_name":"Top Level Namespace","name":"Top Level Namespace","abstract":false,"superclass":null,"ancestors":[],"locations":[],"repository_name":"github.com/lbarasti/statistics","program":true,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":null,"doc":null,"summary":null,"class_methods":[],"constructors":[],"instance_methods":[],"macros":[],"types":[{"html_id":"github.com/lbarasti/statistics/Statistics","path":"Statistics.html","kind":"module","full_name":"Statistics","name":"Statistics","abstract":false,"superclass":null,"ancestors":[],"locations":[{"filename":"lib/distributions.cr","line_number":1,"url":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr"},{"filename":"statistics.cr","line_number":6,"url":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[{"id":"VERSION","name":"VERSION","value":"\"1.0.0\"","doc":null,"summary":null}],"included_modules":[],"extended_modules":[{"html_id":"github.com/lbarasti/statistics/Statistics","kind":"module","full_name":"Statistics","name":"Statistics"}],"subclasses":[],"including_types":[],"namespace":null,"doc":"Basic descriptive statistics functionality.\n\nMore flexible than a scientific-calculator, but not as exhaustive, yet.","summary":"<p>Basic descriptive statistics functionality.</p>","class_methods":[],"constructors":[],"instance_methods":[{"id":"bin_count(values:Enumerable,bins:Int32,min=nil,max=nil,edge:Edge=:left):Bins-instance-method","html_id":"bin_count(values:Enumerable,bins:Int32,min=nil,max=nil,edge:Edge=:left):Bins-instance-method","name":"bin_count","doc":"Counts the number of values in each bin of size `(max - min) / bins`.\n\nReturns a `Bins` object where `edges` and `counts` are ordered by edge.\n\nNOTE: Any empty bin will also be included.\n\nParameters\n- values: a one-dimensional dataset.\n- bins: the number of equally-sized bins to divide the datapoints into.\n- min: the left end of the first bin's edge. 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Default is `:left`.","summary":"<p>Counts the number of values in each bin of size <code>(max - min) / bins</code>.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"},{"name":"bins","doc":null,"default_value":"","external_name":"bins","restriction":"Int32"},{"name":"min","doc":null,"default_value":"nil","external_name":"min","restriction":""},{"name":"max","doc":null,"default_value":"nil","external_name":"max","restriction":""},{"name":"edge","doc":null,"default_value":":left","external_name":"edge","restriction":"Edge"}],"args_string":"(values : Enumerable, bins : Int32, min = <span class=\"n\">nil</span>, max = <span class=\"n\">nil</span>, edge : Edge = <span class=\"n\">:left</span>) : Bins","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L67","def":{"name":"bin_count","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"},{"name":"bins","doc":null,"default_value":"","external_name":"bins","restriction":"Int32"},{"name":"min","doc":null,"default_value":"nil","external_name":"min","restriction":""},{"name":"max","doc":null,"default_value":"nil","external_name":"max","restriction":""},{"name":"edge","doc":null,"default_value":":left","external_name":"edge","restriction":"Edge"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Bins","visibility":"Public","body":"if min.nil? || max.nil?\n  sample_min, sample_max = values.minmax\n  if min.nil?\n    min = sample_min\n  end\n  if max.nil?\n    max = sample_max\n  end\nend\ncounter = Array(Int32).new(size: bins, value: 0)\nstep = (max - min) / bins\nvalues.each do |v|\n  idx = v == max ? bins - 1 : ((v - min) / step).floor.to_i\n  __temp_26 = idx\n  counter[__temp_26] = counter[__temp_26] + 1\nend\nedges = Array.new(bins) do |i|\n  min + (i * step)\nend\nadjusted_edges = case edge\nwhen .left?\n  edges\nwhen .centre?\n  edges.map(&.+(step / 2))\nwhen .right?\n  edges.map(&.+(step))\nelse\n  raise(ArgumentError.new(\"Unexpected value\"))\nend\nBins.new(edges: adjusted_edges, counts: counter, step: step)\n"}},{"id":"describe(values)-instance-method","html_id":"describe(values)-instance-method","name":"describe","doc":"Computes several descriptive statistics of the passed array.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes several descriptive statistics of the passed array.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L14","def":{"name":"describe","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nsorted = values.sort\n{mean: mean(values), var: var(values), std: std(values), skewness: skew(values), kurtosis: kurtosis(values), min: sorted.first, middle: middle(sorted), max: sorted.last, q1: quantile(sorted, 0.25, sorted: true), median: median(sorted, sorted: true), q3: quantile(sorted, 0.75, sorted: true)}\n"}},{"id":"frequency(values:Enumerable(T))forallT-instance-method","html_id":"frequency(values:Enumerable(T))forallT-instance-method","name":"frequency","doc":"Computes the number of occurrences of each value in the dataset.\n\nReturns a Hash with each the dataset values as keys and the number of times they appear as value.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the number of occurrences of each value in the dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable(T)"}],"args_string":"(values : Enumerable(T)) forall T","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L38","def":{"name":"frequency","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable(T)"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"values.reduce(Hash(T, Int32).new(0)) do |freq, v|\n  __temp_24 = v\n  freq[__temp_24] = freq[__temp_24] + 1\n  freq\nend"}},{"id":"kurtosis(values,corrected=false,excess=false)-instance-method","html_id":"kurtosis(values,corrected=false,excess=false)-instance-method","name":"kurtosis","doc":"Computes the kurtosis of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- corrected: when set to `true`, then the calculations are corrected for statistical bias. Default is `false`.\n- excess: when set to `true`, computes the [excess kurtosis](https://en.wikipedia.org/wiki/Kurtosis#Excess_kurtosis). Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1142).","summary":"<p>Computes the kurtosis of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>, excess = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L105","def":{"name":"kurtosis","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm4 = moment(values, m, 4)\nm2 = moment(values, m, 2)\nkurt = if corrected\n  (((1 / (n - 2)) / (n - 3)) * (((((n ** 2) - 1) * m4) / (m2 ** 2)) - (3 * ((n - 1) ** 2)))) + 3\nelse\n  m4 / (m2 ** 2)\nend\nexcess ? kurt - 3 : kurt\n"}},{"id":"mean(values)-instance-method","html_id":"mean(values)-instance-method","name":"mean","doc":"Computes the mean of a dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the mean of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L124","def":{"name":"mean","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(values.reduce(0) do |acc, v|\n  acc + v\nend) / values.size"}},{"id":"median(values,sorted=false)-instance-method","html_id":"median(values,sorted=false)-instance-method","name":"median","doc":"Computes the median of all elements in a dataset.\n\nFor an even number of elements the mean of the two median elements will be computed.\n\nParameters\n- values: a one-dimensional dataset.\n- sorted: when `true`, the computations assume that the provided values are\n  sorted. Default is `false`.\n\nSee Julia's [Statistics.median](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.median).","summary":"<p>Computes the median of all elements in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L138","def":{"name":"median","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nmid = size // 2\nsorted_values = sorted ? values : values.sort\nif size.odd?\n  sorted_values[mid]\nelse\n  middle([sorted_values[mid - 1], sorted_values[mid]])\nend\n"}},{"id":"middle(a,b)-instance-method","html_id":"middle(a,b)-instance-method","name":"middle","doc":"Computes the middle of two values `a` and `b`.","summary":"<p>Computes the middle of two values <code>a</code> and <code>b</code>.</p>","abstract":false,"args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"args_string":"(a, b)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L163","def":{"name":"middle","args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"0.5 * (a + b)"}},{"id":"middle(values)-instance-method","html_id":"middle(values)-instance-method","name":"middle","doc":"Computes the middle of an array `a`, which consists of finding its\nextrema and then computing their mean.\n\nParameters\n- values: a one-dimensional dataset.\n\nSee Julia's [Statistics.middle](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.middle).","summary":"<p>Computes the middle of an array <code>a</code>, which consists of finding its extrema and then computing their mean.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L157","def":{"name":"middle","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min, max = values.minmax\nmiddle(min, max)\n"}},{"id":"mode(values:Enumerable)-instance-method","html_id":"mode(values:Enumerable)-instance-method","name":"mode","doc":"Computes the modal (most common) value in a dataset.\n\nReturns a pair with the modal value and the bin-count for the modal bin.\nIf there is more than one such value, no guarantees are made which one will be picked.\nNOTE: Computing the mode requires traversing the entire dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the modal (most common) value in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"args_string":"(values : Enumerable)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L175","def":{"name":"mode","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(frequency(values)).max_by(&.last)"}},{"id":"moment(values,mean=nil,n=1)-instance-method","html_id":"moment(values,mean=nil,n=1)-instance-method","name":"moment","doc":"Calculates the n-th moment about the mean for a sample.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- n: order of central moment that is returned. Default is `1`.","summary":"<p>Calculates the n-th moment about the mean for a sample.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, n = <span class=\"n\">1</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L186","def":{"name":"moment","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"m = mean || (Statistics.mean(values))\n(values.reduce(0) do |a, b|\n  a + ((b - m) ** n)\nend) / values.size\n"}},{"id":"quantile(values,p,sorted=false)-instance-method","html_id":"quantile(values,p,sorted=false)-instance-method","name":"quantile","doc":"Computes the quantile of a dataset at a specified probability `p` on the interval [0,1].\n\nQuantiles are computed via linear interpolation between the points `((k-1)/(n-1), v[k])`,\nfor `k = 1:n` where `n = values.size`.\n\nParameters\n- values: a one-dimensional dataset.\n- p: probability. Values of `p` should be in the interval `[0, 1]`.\n- sorted indicates whether values can be assumed to be sorted.\n\nImplementation based on Julia's [Statistics.quantile](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.quantile).","summary":"<p>Computes the quantile of a dataset at a specified probability <code>p</code> on the interval [0,1].</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, p, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L202","def":{"name":"quantile","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sorted_values = sorted ? values : values.sort\nn = values.size\naleph = (n - 1) * p\nj = (clamp(aleph.floor, 0, n - 2)).to_i\ngamma = clamp(aleph - j, 0, 1)\na = sorted_values[j]\nb = sorted_values[j + 1]\na + ((b - a) * gamma)\n"}},{"id":"skew(values,corrected=false)-instance-method","html_id":"skew(values,corrected=false)-instance-method","name":"skew","doc":"Computes the skewness of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- corrected: when set to `true`, then the calculations are corrected for statistical bias. Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1039).","summary":"<p>Computes the skewness of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L222","def":{"name":"skew","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm3 = moment(values, m, 3)\nm2 = moment(values, m, 2)\ncorrection_factor = corrected ? (Math.sqrt((n - 1.0) * n)) / (n - 2.0) : 1\n(correction_factor * m3) / (m2 ** 1.5)\n"}},{"id":"std(values,mean=nil,corrected=false)-instance-method","html_id":"std(values,mean=nil,corrected=false)-instance-method","name":"std","doc":"Computes the standard deviation of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. Default is `false`.","summary":"<p>Computes the standard deviation of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L240","def":{"name":"std","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Math.sqrt(var(values, mean, corrected))"}},{"id":"var(values,mean=nil,corrected=false)-instance-method","html_id":"var(values,mean=nil,corrected=false)-instance-method","name":"var","doc":"Computes the variance of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. Default is `false`.","summary":"<p>Computes the variance of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, corrected = <span 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diff --git a/docs/search-index.js b/docs/search-index.js
index 11af590..3eb3871 100644
--- a/docs/search-index.js
+++ b/docs/search-index.js
@@ -1 +1 @@
-crystal_doc_search_index_callback({"repository_name":"github.com/lbarasti/statistics","body":"[![GitHub release](https://img.shields.io/github/release/lbarasti/statistics.svg)](https://github.com/lbarasti/statistics/releases)\n![Build Status](https://github.com/lbarasti/statistics/workflows/build/badge.svg)\n[![License](https://img.shields.io/badge/license-MIT-blue.svg)](https://opensource.org/licenses/MIT)\n\n# statistics\n\nA statistical library to perform descriptive statistics and generate random values based on popular probability distributions.\n\n## Installation\n\n1. Add the dependency to your `shard.yml`:\n\n```yaml\ndependencies:\n  statistics:\n    github: lbarasti/statistics\n```\n\n2. Run `shards install`\n\n## Usage\n\n```crystal\nrequire \"statistics\"\n```\n\n### Descriptive statistics\nYou can compute mean, variance and standard deviation of a collection as follows.\n```crystal\ninclude Statistics\n\nx = [1, 10, 7]\nmean(x) # 6\nvar(x) # 14\nstd(x) # 3.7416...\n```\n\nIf you'd like to know a bit more about your dataset, you can simply `describe` it\n\n```crystal\nx = (1..1000).map { rand }.to_a # a uniformely distributed dataset\ndescribe(x)\n# {\n#   mean: 0.48, var: 0.08, std: 0.28, \n#   skewness: 0.04, kurtosis: 1.81, \n#   min: 0.01, middle: 0.49, max: 0.99, \n#   q1: 0.24, median: 0.49, q3: 0.73\n# }\n```\n\n`Statistics.describe` returns a `NamedTuple`, so you can extract any value via indexing:\n\n```crystal\nstats = describe(x)\nstats[:q1] # returns the first quartile of your sample\n```\n\nFor a complete list of the statistical functions provided, including `quantile`, `moment` and `skew`, check out the [docs](https://lbarasti.com/statistics/Statistics.html).\n\n### Sampling\nTo work with distributions, import the `Distributions` namespace as follows.\n```crystal\ninclude Statistics::Distributions\n```\n\nNow, here is how we sample values from a normal distribution with `mean = 1.5` and `std = 0.2`.\n```crystal\nNormal.new(1.5, 0.2).rand\n```\n\nWe can generate an iterable of normally distributed random values as follows.\n```crystal\ngen = Normal.new(1.5, 0.2)\n1000.times.map { gen.rand }\n```\n\n#### Supported distributions\nThe following distributions are supported:\n* Constant\n* Exponential\n* Normal\n* Poisson\n* Uniform\n\nDon't see your favourite one on the list? Just fork the repo, add your distribution to the `distributions.cr` file, and open a PR.\n\n## Development\n\nThis shard is a work in progress. Everyone's contribution is welcome.\n\nThe guiding principle at this stage is\n> make it work before you make it right\n\nWhich in this context means: let's not focus on benchmarks and performance, but rather on usability and correctness.\n\n## References\n* [numpy.random](https://numpy.org/devdocs/reference/random/generator.html): distributions and random sampling\n* [numpy statistics](https://numpy.org/devdocs/reference/routines.statistics.html#averages-and-variances): order statistics, averages and variances\n* [scipy stats](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py) module and related [tests](https://github.com/scipy/scipy/blob/1150c4c033899a5a4556b7d34d6b137352b36b9e/scipy/stats/tests/test_stats.py) tests\n* [julia random](https://docs.julialang.org/en/v1/stdlib/Random/) module\n* [julia statistics](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.std) module\n* [julia distributions](https://juliastats.org/Distributions.jl/latest/starting/) package.\n* on [skewness and kurtosis](https://brownmath.com/stat/shape.htm), by Stan Brown\n* more on [skewness and kurtosis](https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm), from NIST.\n\n## Contributing\n\n1. Fork it (<https://github.com/lbarasti/statistics/fork>)\n2. Create your feature branch (`git checkout -b my-new-feature`)\n3. Commit your changes (`git commit -am 'Add some feature'`)\n4. Push to the branch (`git push origin my-new-feature`)\n5. 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Default is `false`.\n- excess: when set to `true`, computes the [excess kurtosis](https://en.wikipedia.org/wiki/Kurtosis#Excess_kurtosis). Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1142).","summary":"<p>Computes the kurtosis of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>, excess = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L84","def":{"name":"kurtosis","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm4 = moment(values, m, 4)\nm2 = moment(values, m, 2)\nkurt = if corrected\n  (((1 / (n - 2)) / (n - 3)) * (((((n ** 2) - 1) * m4) / (m2 ** 2)) - (3 * ((n - 1) ** 2)))) + 3\nelse\n  m4 / (m2 ** 2)\nend\nexcess ? kurt - 3 : kurt\n"}},{"id":"mean(values)-instance-method","html_id":"mean(values)-instance-method","name":"mean","doc":"Computes the mean of a dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the mean of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L103","def":{"name":"mean","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(values.reduce(0) do |acc, v|\n  acc + v\nend) / values.size"}},{"id":"median(values,sorted=false)-instance-method","html_id":"median(values,sorted=false)-instance-method","name":"median","doc":"Computes the median of all elements in a dataset.\n\nFor an even number of elements the mean of the two median elements will be computed.\n\nParameters\n- values: a one-dimensional dataset.\n- sorted: when `true`, the computations assume that the provided values are\n  sorted. Default is `false`.\n\nSee Julia's [Statistics.median](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.median).","summary":"<p>Computes the median of all elements in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L117","def":{"name":"median","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nmid = size // 2\nsorted_values = sorted ? values : values.sort\nif size.odd?\n  sorted_values[mid]\nelse\n  middle([sorted_values[mid - 1], sorted_values[mid]])\nend\n"}},{"id":"middle(a,b)-instance-method","html_id":"middle(a,b)-instance-method","name":"middle","doc":"Computes the middle of two values `a` and `b`.","summary":"<p>Computes the middle of two values <code>a</code> and <code>b</code>.</p>","abstract":false,"args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"args_string":"(a, b)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L142","def":{"name":"middle","args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"0.5 * (a + b)"}},{"id":"middle(values)-instance-method","html_id":"middle(values)-instance-method","name":"middle","doc":"Computes the middle of an array `a`, which consists of finding its\nextrema and then computing their mean.\n\nParameters\n- values: a one-dimensional dataset.\n\nSee Julia's [Statistics.middle](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.middle).","summary":"<p>Computes the middle of an array <code>a</code>, which consists of finding its extrema and then computing their mean.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L136","def":{"name":"middle","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min, max = values.minmax\nmiddle(min, max)\n"}},{"id":"mode(values:Enumerable)-instance-method","html_id":"mode(values:Enumerable)-instance-method","name":"mode","doc":"Computes the modal (most common) value in a dataset.\n\nReturns a pair with the modal value and the bin-count for the modal bin.\nIf there is more than one such value, no guarantees are made which one will be picked.\nNOTE: Computing the mode requires traversing the entire dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the modal (most common) value in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"args_string":"(values : Enumerable)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L154","def":{"name":"mode","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(frequency(values)).max_by(&.last)"}},{"id":"moment(values,mean=nil,n=1)-instance-method","html_id":"moment(values,mean=nil,n=1)-instance-method","name":"moment","doc":"Calculates the n-th moment about the mean for a sample.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- n: order of central moment that is returned. Default is `1`.","summary":"<p>Calculates the n-th moment about the mean for a sample.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, n = <span class=\"n\">1</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L165","def":{"name":"moment","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"m = mean || (Statistics.mean(values))\n(values.reduce(0) do |a, b|\n  a + ((b - m) ** n)\nend) / values.size\n"}},{"id":"quantile(values,p,sorted=false)-instance-method","html_id":"quantile(values,p,sorted=false)-instance-method","name":"quantile","doc":"Computes the quantile of a dataset at a specified probability `p` on the interval [0,1].\n\nQuantiles are computed via linear interpolation between the points `((k-1)/(n-1), v[k])`,\nfor `k = 1:n` where `n = values.size`.\n\nParameters\n- values: a one-dimensional dataset.\n- p: probability. Values of `p` should be in the interval `[0, 1]`.\n- sorted indicates whether values can be assumed to be sorted.\n\nImplementation based on Julia's [Statistics.quantile](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.quantile).","summary":"<p>Computes the quantile of a dataset at a specified probability <code>p</code> on the interval [0,1].</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, p, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L181","def":{"name":"quantile","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sorted_values = sorted ? values : values.sort\nn = values.size\naleph = (n - 1) * p\nj = (clamp(aleph.floor, 0, n - 2)).to_i\ngamma = clamp(aleph - j, 0, 1)\na = sorted_values[j]\nb = sorted_values[j + 1]\na + ((b - a) * gamma)\n"}},{"id":"skew(values,corrected=false)-instance-method","html_id":"skew(values,corrected=false)-instance-method","name":"skew","doc":"Computes the skewness of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- corrected: when set to `true`, then the calculations are corrected for statistical bias. Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1039).","summary":"<p>Computes the skewness of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L201","def":{"name":"skew","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm3 = moment(values, m, 3)\nm2 = moment(values, m, 2)\ncorrection_factor = corrected ? (Math.sqrt((n - 1.0) * n)) / (n - 2.0) : 1\n(correction_factor * m3) / (m2 ** 1.5)\n"}},{"id":"std(values,mean=nil,corrected=false)-instance-method","html_id":"std(values,mean=nil,corrected=false)-instance-method","name":"std","doc":"Computes the standard deviation of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. Default is `false`.","summary":"<p>Computes the standard deviation of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/statistics.cr#L219","def":{"name":"std","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Math.sqrt(var(values, mean, corrected))"}},{"id":"var(values,mean=nil,corrected=false)-instance-method","html_id":"var(values,mean=nil,corrected=false)-instance-method","name":"var","doc":"Computes the variance of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. 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correction_factor\n"}}],"macros":[],"types":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions","path":"Statistics/Distributions.html","kind":"module","full_name":"Statistics::Distributions","name":"Distributions","abstract":false,"superclass":null,"ancestors":[],"locations":[{"filename":"lib/distributions.cr","line_number":2,"url":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":{"html_id":"github.com/lbarasti/statistics/Statistics","kind":"module","full_name":"Statistics","name":"Statistics"},"doc":null,"summary":null,"class_methods":[],"constructors":[],"instance_methods":[],"macros":[],"types":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Constant","path":"Statistics/Distributions/Constant.html","kind":"class","full_name":"Statistics::Distributions::Constant","name":"Constant","abstract":false,"superclass":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Distribution","kind":"class","full_name":"Statistics::Distributions::Distribution","name":"Distribution"},"ancestors":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Distribution","kind":"class","full_name":"Statistics::Distributions::Distribution","name":"Distribution"},{"html_id":"github.com/lbarasti/statistics/Reference","kind":"class","full_name":"Reference","name":"Reference"},{"html_id":"github.com/lbarasti/statistics/Object","kind":"class","full_name":"Object","name":"Object"}],"locations":[{"filename":"lib/distributions.cr","line_number":9,"url":"https://github.com/lbarasti/statistics/blob/24ac181e033bb39fd1f8fb99b4ffb8ec125d9cc4/src/lib/distributions.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions","kind":"module","full_name":"Statistics::Distributions","name":"Distributions"},"doc":"Represents 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+crystal_doc_search_index_callback({"repository_name":"github.com/lbarasti/statistics","body":"[![GitHub release](https://img.shields.io/github/release/lbarasti/statistics.svg)](https://github.com/lbarasti/statistics/releases)\n![Build Status](https://github.com/lbarasti/statistics/workflows/build/badge.svg)\n[![License](https://img.shields.io/badge/license-MIT-blue.svg)](https://opensource.org/licenses/MIT)\n\n# statistics\n\nA statistical library to perform descriptive statistics and generate random values based on popular probability distributions.\n\n## Installation\n\n1. Add the dependency to your `shard.yml`:\n\n```yaml\ndependencies:\n  statistics:\n    github: lbarasti/statistics\n```\n\n2. Run `shards install`\n\n## Usage\n\n```crystal\nrequire \"statistics\"\n```\n\n### Descriptive statistics\nYou can compute mean, variance and standard deviation of a collection as follows.\n```crystal\ninclude Statistics\n\nx = [1, 10, 7]\nmean(x) # 6\nvar(x) # 14\nstd(x) # 3.7416...\n```\n\nIf you'd like to know a bit more about your dataset, you can simply `describe` it\n\n```crystal\nx = (1..1000).map { rand }.to_a # a uniformely distributed dataset\ndescribe(x)\n# {\n#   mean: 0.48, var: 0.08, std: 0.28, \n#   skewness: 0.04, kurtosis: 1.81, \n#   min: 0.01, middle: 0.49, max: 0.99, \n#   q1: 0.24, median: 0.49, q3: 0.73\n# }\n```\n\n`Statistics.describe` returns a `NamedTuple`, so you can extract any value via indexing:\n\n```crystal\nstats = describe(x)\nstats[:q1] # returns the first quartile of your sample\n```\n\nFor a complete list of the statistical functions provided, including `quantile`, `moment` and `skew`, check out the [docs](https://lbarasti.com/statistics/Statistics.html).\n\n### Sampling\nTo work with distributions, import the `Distributions` namespace as follows.\n```crystal\ninclude Statistics::Distributions\n```\n\nNow, here is how we sample values from a normal distribution with `mean = 1.5` and `std = 0.2`.\n```crystal\nNormal.new(1.5, 0.2).rand\n```\n\nWe can generate an iterable of normally distributed random values as follows.\n```crystal\ngen = Normal.new(1.5, 0.2)\n1000.times.map { gen.rand }\n```\n\n#### Supported distributions\nThe following distributions are supported:\n* Constant\n* Exponential\n* Normal\n* Poisson\n* Uniform\n\nDon't see your favourite one on the list? Just fork the repo, add your distribution to the `distributions.cr` file, and open a PR.\n\n## Development\n\nThis shard is a work in progress. Everyone's contribution is welcome.\n\nThe guiding principle at this stage is\n> make it work before you make it right\n\nWhich in this context means: let's not focus on benchmarks and performance, but rather on usability and correctness.\n\n## References\n* [numpy.random](https://numpy.org/devdocs/reference/random/generator.html): distributions and random sampling\n* [numpy statistics](https://numpy.org/devdocs/reference/routines.statistics.html#averages-and-variances): order statistics, averages and variances\n* [scipy stats](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py) module and related [tests](https://github.com/scipy/scipy/blob/1150c4c033899a5a4556b7d34d6b137352b36b9e/scipy/stats/tests/test_stats.py) tests\n* [julia random](https://docs.julialang.org/en/v1/stdlib/Random/) module\n* [julia statistics](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.std) module\n* [julia distributions](https://juliastats.org/Distributions.jl/latest/starting/) package.\n* on [skewness and kurtosis](https://brownmath.com/stat/shape.htm), by Stan Brown\n* more on [skewness and kurtosis](https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm), from NIST.\n\n## Contributing\n\n1. 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Default is `:left`.","summary":"<p>Counts the number of values in each bin of size <code>(max - min) / bins</code>.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"},{"name":"bins","doc":null,"default_value":"","external_name":"bins","restriction":"Int32"},{"name":"min","doc":null,"default_value":"nil","external_name":"min","restriction":""},{"name":"max","doc":null,"default_value":"nil","external_name":"max","restriction":""},{"name":"edge","doc":null,"default_value":":left","external_name":"edge","restriction":"Edge"}],"args_string":"(values : Enumerable, bins : Int32, min = <span class=\"n\">nil</span>, max = <span class=\"n\">nil</span>, edge : Edge = <span class=\"n\">:left</span>) : Bins","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L67","def":{"name":"bin_count","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"},{"name":"bins","doc":null,"default_value":"","external_name":"bins","restriction":"Int32"},{"name":"min","doc":null,"default_value":"nil","external_name":"min","restriction":""},{"name":"max","doc":null,"default_value":"nil","external_name":"max","restriction":""},{"name":"edge","doc":null,"default_value":":left","external_name":"edge","restriction":"Edge"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Bins","visibility":"Public","body":"if min.nil? || max.nil?\n  sample_min, sample_max = values.minmax\n  if min.nil?\n    min = sample_min\n  end\n  if max.nil?\n    max = sample_max\n  end\nend\ncounter = Array(Int32).new(size: bins, value: 0)\nstep = (max - min) / bins\nvalues.each do |v|\n  idx = v == max ? bins - 1 : ((v - min) / step).floor.to_i\n  __temp_26 = idx\n  counter[__temp_26] = counter[__temp_26] + 1\nend\nedges = Array.new(bins) do |i|\n  min + (i * step)\nend\nadjusted_edges = case edge\nwhen .left?\n  edges\nwhen .centre?\n  edges.map(&.+(step / 2))\nwhen .right?\n  edges.map(&.+(step))\nelse\n  raise(ArgumentError.new(\"Unexpected value\"))\nend\nBins.new(edges: adjusted_edges, counts: counter, step: step)\n"}},{"id":"describe(values)-instance-method","html_id":"describe(values)-instance-method","name":"describe","doc":"Computes several descriptive statistics of the passed array.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes several descriptive statistics of the passed array.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L14","def":{"name":"describe","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nsorted = values.sort\n{mean: mean(values), var: var(values), std: std(values), skewness: skew(values), kurtosis: kurtosis(values), min: sorted.first, middle: middle(sorted), max: sorted.last, q1: quantile(sorted, 0.25, sorted: true), median: median(sorted, sorted: true), q3: quantile(sorted, 0.75, sorted: true)}\n"}},{"id":"frequency(values:Enumerable(T))forallT-instance-method","html_id":"frequency(values:Enumerable(T))forallT-instance-method","name":"frequency","doc":"Computes the number of occurrences of each value in the dataset.\n\nReturns a Hash with each the dataset values as keys and the number of times they appear as value.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the number of occurrences of each value in the dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable(T)"}],"args_string":"(values : Enumerable(T)) forall T","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L38","def":{"name":"frequency","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable(T)"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"values.reduce(Hash(T, Int32).new(0)) do |freq, v|\n  __temp_24 = v\n  freq[__temp_24] = freq[__temp_24] + 1\n  freq\nend"}},{"id":"kurtosis(values,corrected=false,excess=false)-instance-method","html_id":"kurtosis(values,corrected=false,excess=false)-instance-method","name":"kurtosis","doc":"Computes the kurtosis of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- corrected: when set to `true`, then the calculations are corrected for statistical bias. Default is `false`.\n- excess: when set to `true`, computes the [excess kurtosis](https://en.wikipedia.org/wiki/Kurtosis#Excess_kurtosis). Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1142).","summary":"<p>Computes the kurtosis of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>, excess = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L105","def":{"name":"kurtosis","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""},{"name":"excess","doc":null,"default_value":"false","external_name":"excess","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm4 = moment(values, m, 4)\nm2 = moment(values, m, 2)\nkurt = if corrected\n  (((1 / (n - 2)) / (n - 3)) * (((((n ** 2) - 1) * m4) / (m2 ** 2)) - (3 * ((n - 1) ** 2)))) + 3\nelse\n  m4 / (m2 ** 2)\nend\nexcess ? kurt - 3 : kurt\n"}},{"id":"mean(values)-instance-method","html_id":"mean(values)-instance-method","name":"mean","doc":"Computes the mean of a dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the mean of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L124","def":{"name":"mean","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(values.reduce(0) do |acc, v|\n  acc + v\nend) / values.size"}},{"id":"median(values,sorted=false)-instance-method","html_id":"median(values,sorted=false)-instance-method","name":"median","doc":"Computes the median of all elements in a dataset.\n\nFor an even number of elements the mean of the two median elements will be computed.\n\nParameters\n- values: a one-dimensional dataset.\n- sorted: when `true`, the computations assume that the provided values are\n  sorted. Default is `false`.\n\nSee Julia's [Statistics.median](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.median).","summary":"<p>Computes the median of all elements in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L138","def":{"name":"median","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nmid = size // 2\nsorted_values = sorted ? values : values.sort\nif size.odd?\n  sorted_values[mid]\nelse\n  middle([sorted_values[mid - 1], sorted_values[mid]])\nend\n"}},{"id":"middle(a,b)-instance-method","html_id":"middle(a,b)-instance-method","name":"middle","doc":"Computes the middle of two values `a` and `b`.","summary":"<p>Computes the middle of two values <code>a</code> and <code>b</code>.</p>","abstract":false,"args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"args_string":"(a, b)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L163","def":{"name":"middle","args":[{"name":"a","doc":null,"default_value":"","external_name":"a","restriction":""},{"name":"b","doc":null,"default_value":"","external_name":"b","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"0.5 * (a + b)"}},{"id":"middle(values)-instance-method","html_id":"middle(values)-instance-method","name":"middle","doc":"Computes the middle of an array `a`, which consists of finding its\nextrema and then computing their mean.\n\nParameters\n- values: a one-dimensional dataset.\n\nSee Julia's [Statistics.middle](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.middle).","summary":"<p>Computes the middle of an array <code>a</code>, which consists of finding its extrema and then computing their mean.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L157","def":{"name":"middle","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min, max = values.minmax\nmiddle(min, max)\n"}},{"id":"mode(values:Enumerable)-instance-method","html_id":"mode(values:Enumerable)-instance-method","name":"mode","doc":"Computes the modal (most common) value in a dataset.\n\nReturns a pair with the modal value and the bin-count for the modal bin.\nIf there is more than one such value, no guarantees are made which one will be picked.\nNOTE: Computing the mode requires traversing the entire dataset.\n\nParameters\n- values: a one-dimensional dataset.","summary":"<p>Computes the modal (most common) value in a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"args_string":"(values : Enumerable)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L175","def":{"name":"mode","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Enumerable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(frequency(values)).max_by(&.last)"}},{"id":"moment(values,mean=nil,n=1)-instance-method","html_id":"moment(values,mean=nil,n=1)-instance-method","name":"moment","doc":"Calculates the n-th moment about the mean for a sample.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- n: order of central moment that is returned. Default is `1`.","summary":"<p>Calculates the n-th moment about the mean for a sample.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, n = <span class=\"n\">1</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L186","def":{"name":"moment","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"n","doc":null,"default_value":"1","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"m = mean || (Statistics.mean(values))\n(values.reduce(0) do |a, b|\n  a + ((b - m) ** n)\nend) / values.size\n"}},{"id":"quantile(values,p,sorted=false)-instance-method","html_id":"quantile(values,p,sorted=false)-instance-method","name":"quantile","doc":"Computes the quantile of a dataset at a specified probability `p` on the interval [0,1].\n\nQuantiles are computed via linear interpolation between the points `((k-1)/(n-1), v[k])`,\nfor `k = 1:n` where `n = values.size`.\n\nParameters\n- values: a one-dimensional dataset.\n- p: probability. Values of `p` should be in the interval `[0, 1]`.\n- sorted indicates whether values can be assumed to be sorted.\n\nImplementation based on Julia's [Statistics.quantile](https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.quantile).","summary":"<p>Computes the quantile of a dataset at a specified probability <code>p</code> on the interval [0,1].</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"args_string":"(values, p, sorted = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L202","def":{"name":"quantile","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"p","doc":null,"default_value":"","external_name":"p","restriction":""},{"name":"sorted","doc":null,"default_value":"false","external_name":"sorted","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sorted_values = sorted ? values : values.sort\nn = values.size\naleph = (n - 1) * p\nj = (clamp(aleph.floor, 0, n - 2)).to_i\ngamma = clamp(aleph - j, 0, 1)\na = sorted_values[j]\nb = sorted_values[j + 1]\na + ((b - a) * gamma)\n"}},{"id":"skew(values,corrected=false)-instance-method","html_id":"skew(values,corrected=false)-instance-method","name":"skew","doc":"Computes the skewness of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- corrected: when set to `true`, then the calculations are corrected for statistical bias. Default is `false`.\n\nThis implementation is based on the [scipy/stats.py](https://github.com/scipy/scipy/blob/3de0d58/scipy/stats/stats.py#L1039).","summary":"<p>Computes the skewness of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L222","def":{"name":"skew","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"n = values.size\nm = mean(values)\nm3 = moment(values, m, 3)\nm2 = moment(values, m, 2)\ncorrection_factor = corrected ? (Math.sqrt((n - 1.0) * n)) / (n - 2.0) : 1\n(correction_factor * m3) / (m2 ** 1.5)\n"}},{"id":"std(values,mean=nil,corrected=false)-instance-method","html_id":"std(values,mean=nil,corrected=false)-instance-method","name":"std","doc":"Computes the standard deviation of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. Default is `false`.","summary":"<p>Computes the standard deviation of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, corrected = <span class=\"n\">false</span>)","source_link":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/statistics.cr#L240","def":{"name":"std","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Math.sqrt(var(values, mean, corrected))"}},{"id":"var(values,mean=nil,corrected=false)-instance-method","html_id":"var(values,mean=nil,corrected=false)-instance-method","name":"var","doc":"Computes the variance of a dataset.\n\nParameters\n- values: a one-dimensional dataset.\n- mean: a pre-computed mean. This could be a pre-computed sample's mean\n  or the population's known mean. If a mean is not provided, then the sample's\n  mean will be computed. Default is `nil`.\n- corrected: when set to `true`, then the sum of squares is scaled\n  with `values.size - 1`, rather than with `values.size`. Default is `false`.","summary":"<p>Computes the variance of a dataset.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""},{"name":"mean","doc":null,"default_value":"nil","external_name":"mean","restriction":""},{"name":"corrected","doc":null,"default_value":"false","external_name":"corrected","restriction":""}],"args_string":"(values, mean = <span class=\"n\">nil</span>, corrected = <span 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@mean\n"}}],"macros":[],"types":[]},{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Poisson","path":"Statistics/Distributions/Poisson.html","kind":"class","full_name":"Statistics::Distributions::Poisson","name":"Poisson","abstract":false,"superclass":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution","kind":"class","full_name":"Statistics::Distributions::DiscreteDistribution","name":"DiscreteDistribution"},"ancestors":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/DiscreteDistribution","kind":"class","full_name":"Statistics::Distributions::DiscreteDistribution","name":"DiscreteDistribution"},{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Distribution","kind":"class","full_name":"Statistics::Distributions::Distribution","name":"Distribution"},{"html_id":"github.com/lbarasti/statistics/Reference","kind":"class","full_name":"Reference","name":"Reference"},{"html_id":"github.com/lbarasti/statistics/Object","kind":"class","full_name":"Object","name":"Object"}],"locations":[{"filename":"lib/distributions.cr","line_number":107,"url":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions","kind":"module","full_name":"Statistics::Distributions","name":"Distributions"},"doc":"Represents 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p\nend\nx\n"}}],"macros":[],"types":[]},{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Uniform","path":"Statistics/Distributions/Uniform.html","kind":"class","full_name":"Statistics::Distributions::Uniform","name":"Uniform","abstract":false,"superclass":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution","kind":"class","full_name":"Statistics::Distributions::ContinuousDistribution","name":"ContinuousDistribution"},"ancestors":[{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/ContinuousDistribution","kind":"class","full_name":"Statistics::Distributions::ContinuousDistribution","name":"ContinuousDistribution"},{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions/Distribution","kind":"class","full_name":"Statistics::Distributions::Distribution","name":"Distribution"},{"html_id":"github.com/lbarasti/statistics/Reference","kind":"class","full_name":"Reference","name":"Reference"},{"html_id":"github.com/lbarasti/statistics/Object","kind":"class","full_name":"Object","name":"Object"}],"locations":[{"filename":"lib/distributions.cr","line_number":143,"url":"https://github.com/lbarasti/statistics/blob/420c1a706c1cab85e7c2a5f128c125a787149471/src/lib/distributions.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[],"included_modules":[],"extended_modules":[],"subclasses":[],"including_types":[],"namespace":{"html_id":"github.com/lbarasti/statistics/Statistics/Distributions","kind":"module","full_name":"Statistics::Distributions","name":"Distributions"},"doc":"Represents 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\ No newline at end of file
diff --git a/shard.yml b/shard.yml
index 81dce4a..4ad9228 100644
--- a/shard.yml
+++ b/shard.yml
@@ -1,5 +1,5 @@
 name: statistics
-version: 0.3.0
+version: 1.0.0
 
 authors:
   - lbarasti <lbarasti@users.noreply.github.com>
diff --git a/src/statistics.cr b/src/statistics.cr
index d50cc41..6f97989 100644
--- a/src/statistics.cr
+++ b/src/statistics.cr
@@ -5,7 +5,7 @@ require "./lib/distributions"
 # More flexible than a scientific-calculator, but not as exhaustive, yet.
 module Statistics
   extend self
-  VERSION = "0.3.0"
+  VERSION = "1.0.0"
 
   # Computes several descriptive statistics of the passed array.
   #