diff --git a/.gitignore b/.gitignore index 0bbd4a9..82f1ad5 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,3 @@ -/docs/ /lib/ /bin/ /.shards/ diff --git a/docs/Statistics.html b/docs/Statistics.html new file mode 100644 index 0000000..84c7d60 --- /dev/null +++ b/docs/Statistics.html @@ -0,0 +1,680 @@ + + + + + + + + + + + + + + Statistics - github.com/lbarasti/statistics + + + + +
+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

+ + module Statistics + +

+ + + + + +

+ + + + Overview +

+ +

Basic descriptive statistics functionality.

+ +

More flexible than a scientific-calculator, but not as exhaustive, yet.

+ + + + + + + +

+ + + + Extended Modules +

+ + + + + + + + + +

+ + + + Defined in: +

+ + + + lib/distributions.cr + + +
+ + + + statistics.cr + + +
+ + + + + +

+ + + + Constant Summary +

+ +
+ +
+ VERSION = "0.1.0" +
+ + +
+ + + + + + + +

+ + + + Instance Method Summary +

+ + + + + + +
+ +
+ + + + + + +

+ + + + Instance Method Detail +

+ +
+
+ + def describe(values) + + # +
+ +
+ +

Computes several descriptive statistics of the passed array.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def frequency(values : Enumerable(T)) forall T + + # +
+ +
+ +

Computes the number of occurrences of each value in the dataset.

+ +

Returns a Hash with each the dataset values as keys and the number of times they appear as value.

+ +

Parameters

+ +
  • values: a one-dimensional dataset
+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def kurtosis(values, corrected = false, excess = false) + + # +
+ +
+ +

Computes the kurtosis of a dataset.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
  • corrected: when set to true, then the calculations are corrected for statistical bias. Default is false.
  • excess: when set to true, computes the excess kurtosis. Default is false.
+ +

This implementation is based on the scipy/stats.py.

+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def mean(values) + + # +
+ +
+ +

Computes the mean of a dataset.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def median(values, sorted = false) + + # +
+ +
+ +

Computes the median of all elements in a dataset.

+ +

For an even number of elements the mean of the two median elements will be computed.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
  • sorted: when true, the computations assume that the provided values are + sorted. Default is false.
+ +

See Julia's Statistics.median.

+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def middle(a, b) + + # +
+ +
+ +

Computes the middle of two values a and b.

+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def middle(values) + + # +
+ +
+ +

Computes the middle of an array a, which consists of finding its +extrema and then computing their mean.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
+ +

See Julia's Statistics.middle.

+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def mode(values : Enumerable) + + # +
+ +
+ +

Computes the modal (most common) value in a dataset.

+ +

Returns a pair with the modal value and the bin-count for the modal bin. +If there is more than one such value, no guarantees are made which one will be picked.

+ +

NOTE computing the mode requires traversing the entire dataset.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def moment(values, mean = nil, n = 1) + + # +
+ +
+ +

Calculates the n-th moment about the mean for a sample.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
  • #mean: a pre-computed mean. If a mean is not provided, then the sample's + mean will be computed. Default is nil.
  • n: Order of central moment that is returned. Default is 1.
+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def quantile(values, p, sorted = false) + + # +
+ +
+ +

Computes the quantile of a dataset at a specified probability p on the interval [0,1].

+ +

Quantiles are computed via linear interpolation between the points ((k-1)/(n-1), v[k]), +for k = 1:n where n = values.size.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
  • p: probability. Values of p should be in the interval [0, 1].
  • sorted indicates whether values can be assumed to be sorted.
+ +

Implementation based on Julia's Statistics.quantile.

+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def skew(values, corrected = false) + + # +
+ +
+ +

Computes the skewness of a dataset.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
  • corrected: when set to true, then the calculations are corrected for statistical bias. Default is false.
+ +

This implementation is based on the scipy/stats.py.

+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def std(values, mean = nil, corrected = false) + + # +
+ +
+ +

Computes the standard deviation of a dataset.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
  • #mean: a pre-computed #mean. This could be a pre-computed sample's mean + or the population's known mean. If a mean is not provided, then the sample's + mean will be computed. Default is nil.
  • corrected: when set to true, then the sum of squares is scaled + with values.size - 1, rather than with values.size. Default is false.
+
+ +
+
+ + [View source] + +
+
+ +
+
+ + def var(values, mean = nil, corrected = false) + + # +
+ +
+ +

Computes the variance of a dataset.

+ +

Parameters

+ +
  • values: a one-dimensional dataset.
  • #mean: a pre-computed #mean. This could be a pre-computed sample's mean + or the population's known mean. If a mean is not provided, then the sample's + mean will be computed. Default is nil.
  • corrected: when set to true, then the sum of squares is scaled + with values.size - 1, rather than with values.size. Default is false.
+
+ +
+
+ + [View source] + +
+
+ + + + + +
+ + + diff --git a/docs/Statistics/Distributions.html b/docs/Statistics/Distributions.html new file mode 100644 index 0000000..763ed2c --- /dev/null +++ b/docs/Statistics/Distributions.html @@ -0,0 +1,162 @@ + + + + + + + + + + + + + + Statistics::Distributions - github.com/lbarasti/statistics + + + + +
+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

+ + module Statistics::Distributions + +

+ + + + + + + + + + + + + + + + + + +

+ + + + Defined in: +

+ + + + lib/distributions.cr + + +
+ + + + + + + + + + + + + + +
+ +
+ + + + + + + + + +
+ + + diff --git a/docs/Statistics/Distributions/Constant.html b/docs/Statistics/Distributions/Constant.html new file mode 100644 index 0000000..c34c673 --- /dev/null +++ b/docs/Statistics/Distributions/Constant.html @@ -0,0 +1,291 @@ + + + + + + + + + + + + + + Statistics::Distributions::Constant - github.com/lbarasti/statistics + + + + +
+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

+ + class Statistics::Distributions::Constant + +

+ + + + + + + + + + + + + + + + + + + + +

+ + + + Defined in: +

+ + + + lib/distributions.cr + + +
+ + + + + + +

+ + + + Constructors +

+ + + + + + +

+ + + + Instance Method Summary +

+ + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
+ + +

+ + + + Constructor Detail +

+ +
+
+ + def self.new(rand : Float64) + + # +
+ +
+
+ + [View source] + +
+
+ + + + + + +

+ + + + Instance Method Detail +

+ +
+
+ + def rand : Float64 + + # +
+ +
+
+ + [View source] + +
+
+ +
+
+ + def rand=(rand) + + # +
+ +
+
+ + [View source] + +
+
+ + + + + +
+ + + diff --git a/docs/Statistics/Distributions/Exponential.html b/docs/Statistics/Distributions/Exponential.html new file mode 100644 index 0000000..3227016 --- /dev/null +++ b/docs/Statistics/Distributions/Exponential.html @@ -0,0 +1,278 @@ + + + + + + + + + + + + + + Statistics::Distributions::Exponential - github.com/lbarasti/statistics + + + + +
+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

+ + class Statistics::Distributions::Exponential + +

+ + + + + + + + + + + + + + + + + + + + +

+ + + + Defined in: +

+ + + + lib/distributions.cr + + +
+ + + + + + +

+ + + + Constructors +

+ + + + + + +

+ + + + Instance Method Summary +

+ + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
+ + +

+ + + + Constructor Detail +

+ +
+
+ + def self.new(lambda : Float64) + + # +
+ +
+ +

https://en.wikipedia.org/wiki/Inverse_transform_sampling +https://stackoverflow.com/questions/2106503/pseudorandom-number-generator-exponential-distribution/2106564

+
+ +
+
+ + [View source] + +
+
+ + + + + + +

+ + + + Instance Method Detail +

+ +
+
+ + def rand + + # +
+ +
+
+ + [View source] + +
+
+ + + + + +
+ + + diff --git a/docs/Statistics/Distributions/Normal.html b/docs/Statistics/Distributions/Normal.html new file mode 100644 index 0000000..41bdf9a --- /dev/null +++ b/docs/Statistics/Distributions/Normal.html @@ -0,0 +1,293 @@ + + + + + + + + + + + + + + Statistics::Distributions::Normal - github.com/lbarasti/statistics + + + + +
+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

+ + class Statistics::Distributions::Normal + +

+ + + + + + + + + + + + + + + + + + + + +

+ + + + Defined in: +

+ + + + lib/distributions.cr + + +
+ + + + + +

+ + + + Constant Summary +

+ +
+ +
+ TWO_PI = 2 * Math::PI +
+ +
+

https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform

+
+ + +
+ + + +

+ + + + Constructors +

+ + + + + + +

+ + + + Instance Method Summary +

+ + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
+ + +

+ + + + Constructor Detail +

+ +
+
+ + def self.new(mean : Float64, std : Float64) + + # +
+ +
+
+ + [View source] + +
+
+ + + + + + +

+ + + + Instance Method Detail +

+ +
+
+ + def rand + + # +
+ +
+
+ + [View source] + +
+
+ + + + + +
+ + + diff --git a/docs/Statistics/Distributions/Poisson.html b/docs/Statistics/Distributions/Poisson.html new file mode 100644 index 0000000..9f7b97e --- /dev/null +++ b/docs/Statistics/Distributions/Poisson.html @@ -0,0 +1,279 @@ + + + + + + + + + + + + + + Statistics::Distributions::Poisson - github.com/lbarasti/statistics + + + + +
+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

+ + class Statistics::Distributions::Poisson + +

+ + + + + + + + + + + + + + + + + + + + +

+ + + + Defined in: +

+ + + + lib/distributions.cr + + +
+ + + + + + +

+ + + + Constructors +

+ + + + + + +

+ + + + Instance Method Summary +

+ + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
+ + +

+ + + + Constructor Detail +

+ +
+
+ + def self.new(lambda : Float64) + + # +
+ +
+ +

see https://en.wikipedia.org/wiki/Poisson_distribution#Generating_Poisson-distributed_random_variables +https://www.johndcook.com/SimpleRNG.cpp +https://www.johndcook.com/blog/2010/06/14/generating-poisson-random-values/

+
+ +
+
+ + [View source] + +
+
+ + + + + + +

+ + + + Instance Method Detail +

+ +
+
+ + def rand + + # +
+ +
+
+ + [View source] + +
+
+ + + + + +
+ + + diff --git a/docs/Statistics/Distributions/Uniform.html b/docs/Statistics/Distributions/Uniform.html new file mode 100644 index 0000000..8358c99 --- /dev/null +++ b/docs/Statistics/Distributions/Uniform.html @@ -0,0 +1,270 @@ + + + + + + + + + + + + + + Statistics::Distributions::Uniform - github.com/lbarasti/statistics + + + + +
+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

+ + class Statistics::Distributions::Uniform + +

+ + + + + + + + + + + + + + + + + + + + +

+ + + + Defined in: +

+ + + + lib/distributions.cr + + +
+ + + + + + +

+ + + + Constructors +

+ + + + + + +

+ + + + Instance Method Summary +

+ + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
+ + +

+ + + + Constructor Detail +

+ +
+
+ + def self.new(min : Float64, max : Float64) + + # +
+ +
+
+ + [View source] + +
+
+ + + + + + +

+ + + + Instance Method Detail +

+ +
+
+ + def rand + + # +
+ +
+
+ + [View source] + +
+
+ + + + + +
+ + + diff --git a/docs/css/style.css b/docs/css/style.css new file mode 100644 index 0000000..a63baf5 --- /dev/null +++ b/docs/css/style.css @@ -0,0 +1,674 @@ +html, body { + background: #FFFFFF; + position: relative; + margin: 0; + padding: 0; + width: 100%; + height: 100%; + overflow: hidden; +} + +body { + font-family: "Avenir", "Tahoma", "Lucida Sans", "Lucida Grande", Verdana, Arial, sans-serif; + color: #333; + line-height: 1.5; +} + +a { + color: #263F6C; +} + +a:visited { + color: #112750; +} + +h1, h2, h3, h4, h5, h6 { + margin: 35px 0 25px; + color: #444444; +} + +h1.type-name { + color: #47266E; + margin: 20px 0 30px; + background-color: #F8F8F8; + padding: 10px 12px; + border: 1px solid #EBEBEB; + border-radius: 2px; +} + +h2 { + border-bottom: 1px solid #E6E6E6; + padding-bottom: 5px; +} + +body { + display: flex; +} + +.sidebar, .main-content { + overflow: auto; +} + +.sidebar { + width: 30em; + color: #F8F4FD; + background-color: #2E1052; + padding: 0 0 30px; + box-shadow: inset -3px 0 4px rgba(0,0,0,.35); + line-height: 1.2; +} + +.sidebar .search-box { + padding: 8px 9px; +} + +.sidebar input { + display: block; + box-sizing: border-box; + margin: 0; + padding: 5px; + font: inherit; + font-family: inherit; + line-height: 1.2; + width: 100%; + border: 0; + outline: 0; + border-radius: 2px; + box-shadow: 0px 3px 5px rgba(0,0,0,.25); + transition: box-shadow .12s; +} + +.sidebar input:focus { + box-shadow: 0px 5px 6px rgba(0,0,0,.5); +} + +.sidebar input::-webkit-input-placeholder { /* Chrome/Opera/Safari */ + color: #C8C8C8; + font-size: 14px; + text-indent: 2px; +} + +.sidebar input::-moz-placeholder { /* Firefox 19+ */ + color: #C8C8C8; + font-size: 14px; + text-indent: 2px; +} + +.sidebar input:-ms-input-placeholder { /* IE 10+ */ + color: #C8C8C8; + font-size: 14px; + text-indent: 2px; +} + +.sidebar input:-moz-placeholder { /* Firefox 18- */ + color: #C8C8C8; + font-size: 14px; + text-indent: 2px; +} + +.sidebar ul { + margin: 0; + padding: 0; + list-style: none outside; +} + +.sidebar li { + display: block; + position: relative; +} + +.types-list li.hide { + display: none; +} + +.sidebar a { + text-decoration: none; + color: inherit; + transition: color .14s; +} +.types-list a { + display: block; + padding: 5px 15px 5px 30px; +} + +.types-list { + display: block; +} + +.sidebar a:focus { + outline: 1px solid #D1B7F1; +} + +.types-list a { + padding: 5px 15px 5px 30px; +} + +.sidebar .current > a, +.sidebar a:hover { + color: #866BA6; +} + +.repository-links { + padding: 5px 15px 5px 30px; +} + +.types-list li ul { + overflow: hidden; + height: 0; + max-height: 0; + transition: 1s ease-in-out; +} + +.types-list li.parent { + padding-left: 30px; +} + +.types-list li.parent::before { + box-sizing: border-box; + content: "▼"; + display: block; + width: 30px; + height: 30px; + position: absolute; + top: 0; + left: 0; + text-align: center; + color: white; + font-size: 8px; + line-height: 30px; + transform: rotateZ(-90deg); + cursor: pointer; + transition: .2s linear; +} + + +.types-list li.parent > a { + padding-left: 0; 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+
+
+ +
+ +
+ README +
+
+ +
+ +
+ +
+ + +
+
+ + +
+

Build Status +License

+ +

+ +statistics

+ +

A statistical library to perform descriptive statistics and generate random values based on popular probability distributions.

+ +

+ +Installation

+ +
  1. Add the dependency to your shard.yml:
+ +
dependencies:
+  statistics:
+    github: lbarasti/statistics
+ +
  1. Run shards install
+ +

+ +Usage

+ +
require "statistics"
+ +

+ +Descriptive statistics

+ +

You can compute mean, variance and standard deviation of a collection as follows.

+ +
include Statistics
+
+x = [1, 10, 7]
+mean(x) # 6
+var(x) # 14
+var(x, corrected: true) # 21
+var(x, mean: 8) # 18.0
+std(x) # 3.7416...
+ +

+ +Sampling

+ +

To work with distributions, import the Distributions namespace as follows.

+ +
include Statistics::Distributions
+ +

Now, here is how we sample values from a normal distribution with mean = 1.5 and std = 0.2.

+ +
Normal.new(1.5, 0.2).rand
+ +

We can generate an iterable of normally distributed random values as follows.

+ +
gen = Normal.new(1.5, 0.2)
+1000.times.map { gen.rand }
+ +

+ +Supported distributions

+ +

The following distributions are supported:

+ + + +

Don't see your favourite one on the list? Just fork the repo, add your distribution to the distributions.cr file, and open a PR.

+ +

+ +Development

+ +

This shard is a work in progress. Everyone's contribution is welcome.

+ +

The guiding principle at this stage is

+ +
make it work before you make it right
+ +

Which in this context means: let's not focus on benchmarks and performance, but rather on usability and correctness.

+ +

+ +References

+ + + +

+ +Contributing

+ +
  1. Fork it (<https://github.com/lbarasti/statistics/fork>)
  2. Create your feature branch (git checkout -b my-new-feature)
  3. Commit your changes (git commit -am 'Add some feature')
  4. Push to the branch (git push origin my-new-feature)
  5. Create a new Pull Request
+ +

+ +Contributors

+ + +
+ + diff --git a/docs/index.json b/docs/index.json new file mode 100644 index 0000000..c282c0a --- /dev/null +++ b/docs/index.json @@ -0,0 +1 @@ +{"repository_name":"github.com/lbarasti/statistics","body":"![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\nvar(x, corrected: true) # 21\nvar(x, mean: 8) # 18.0\nstd(x) # 3.7416...\n```\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 ()\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/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/lib/distributions.cr"},{"filename":"statistics.cr","line_number":6,"url":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[{"id":"VERSION","name":"VERSION","value":"\"0.1.0\"","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":"

Basic descriptive statistics functionality.

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Computes several descriptive statistics of the passed array.

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Computes the number of occurrences of each value in the dataset.

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Computes the kurtosis of a dataset.

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Computes the mean of a dataset.

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Computes the median of all elements in a dataset.

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Computes the middle of two values a and b.

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Computes the middle of an array a, which consists of finding its extrema and then computing their mean.

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Computes the modal (most common) value in a dataset.

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Calculates the n-th moment about the mean for a sample.

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Computes the quantile of a dataset at a specified probability p on the interval [0,1].

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Computes the skewness of a dataset.

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Computes the standard deviation of a dataset.

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Computes the variance of a dataset.

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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/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/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/Reference","kind":"class","full_name":"Reference","name":"Reference"},"ancestors":[{"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":3,"url":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/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":null,"summary":null,"class_methods":[],"constructors":[{"id":"new(rand:Float64)-class-method","html_id":"new(rand:Float64)-class-method","name":"new","doc":null,"summary":null,"abstract":false,"args":[{"name":"rand","doc":null,"default_value":"","external_name":"rand","restriction":"Float64"}],"args_string":"(rand 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} + if(aIndex >= 0){ + if(bIndex >= 0){ + if(aIndex != bIndex){ + return aIndex > bIndex ? 1 : -1; + } + }else{ + return -1; + } + }else if(bIndex >= 0) { + return 1; + } + } + } + + return 0; + }); + + if (results.length > 1) { + // if we have more than two search terms, only include results with the most matches + var bestMatchedTerms = uniqueArray(results[0].matched_terms).length; + + results = results.filter(function(result) { + return uniqueArray(result.matched_terms).length + 1 >= bestMatchedTerms; + }); + } + return results; +}; + +CrystalDoc.prefixForType = function(type) { + switch (type) { + case "instance_method": + return "#"; + + case "class_method": + case "macro": + case "constructor": + return "."; + + default: + return false; + } +}; + +CrystalDoc.displaySearchResults = function(results, query) { + function sanitize(html){ + return html.replace(/<(?!\/?code)[^>]+>/g, ""); + } + + // limit results + if (results.length > CrystalDoc.MAX_RESULTS_DISPLAY) { + results = results.slice(0, CrystalDoc.MAX_RESULTS_DISPLAY); 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+ var index = normalized.indexOf(term); + if((index == 0) || (index > 0 && normalized[index-1] == ":")){ + return true; + } + } + return false; + } + this.matchesMethod = function(name, kind, type) { + return runMatcher(name, function(normalized, term) { + var i = term.indexOf("#"); + if(i >= 0){ + if (kind != "instance_method") { + return false; + } + }else{ + i = term.indexOf("."); + if(i >= 0){ + if (kind != "class_method" && kind != "macro" && kind != "constructor") { + return false; + } + }else{ + //neither # nor . + if(term.indexOf(":") && namespaceMatcher(normalized, term)){ + return true; + } + } + } + + var methodName = term; + if(i >= 0){ + var termType = term.substring(0, i); + methodName = term.substring(i+1); + + if(termType != "") { + if(CrystalDoc.Query.normalizeTerm(type.full_name).indexOf(termType) < 0){ + return false; + } + } + } + return normalized.indexOf(methodName) >= 0; + }); + }; + + this.matchesNamespace = function(namespace){ + return runMatcher(namespace, namespaceMatcher); + }; + + this.highlight = function(string) { + if (typeof string == "undefined") { + return ""; + } + function escapeRegExp(s) { + return s.replace(/[.*+?\^${}()|\[\]\\]/g, "\\$&").replace(/^[#\.:]+/, ""); + } + return string.replace( + new RegExp("(" + this.normalizedTerms.map(escapeRegExp).join("|") + ")", "gi"), + "$1" + ); + }; +}; +CrystalDoc.Query.normalizeTerm = function(term) { + return term.toLowerCase(); +}; +CrystalDoc.Query.stripModifiers = function(term) { + switch (term[0]) { + case "#": + case ".": + case ":": + return term.substr(1); + + default: + return term; + } +} + +CrystalDoc.search = function(string) { + if(!CrystalDoc.searchIndex) { + console.log("CrystalDoc search index not initialized, delaying search"); + + document.addEventListener("CrystalDoc:loaded", function listener(){ + document.removeEventListener("CrystalDoc:loaded", listener); + CrystalDoc.search(string); + }); + return; + } + + document.dispatchEvent(new Event("CrystalDoc:searchStarted")); + + var query = new CrystalDoc.Query(string); 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+ + var scrollSidebarToOpenType = function(){ + var openTypes = typesList.querySelectorAll('.current'); + if (openTypes.length > 0) { + var lastOpenType = openTypes[openTypes.length - 1]; + lastOpenType.scrollIntoView(); + } + } + + scrollSidebarToOpenType(); + + var setPersistentSearchQuery = function(value){ + sessionStorage.setItem(repositoryName + '::search-input:value', value); + } + + for(var i = 0; i < parents.length; i++) { + var _parent = parents[i]; + _parent.addEventListener('click', function(e) { + e.stopPropagation(); + + if(e.target.tagName.toLowerCase() == 'li') { + if(e.target.className.match(/open/)) { + sessionStorage.removeItem(e.target.getAttribute('data-id')); + e.target.className = e.target.className.replace(/ +open/g, ''); + } else { + sessionStorage.setItem(e.target.getAttribute('data-id'), '1'); + if(e.target.className.indexOf('open') == -1) { + e.target.className += ' open'; + } + } + } + }); + + if(sessionStorage.getItem(_parent.getAttribute('data-id')) == '1') { + _parent.className += ' open'; + } + } + + var leaveSearchScope = function(){ + CrystalDoc.toggleResultsList(false); + window.focus(); + } + + var navigator = new Navigator(document.querySelector('.types-list'), searchInput, document.querySelector(".search-results"), leaveSearchScope); + + CrystalDoc.loadIndex(); + var searchTimeout; + var lastSearchText = false; + var performSearch = function() { + document.dispatchEvent(new Event("CrystalDoc:searchDebounceStarted")); + + clearTimeout(searchTimeout); + searchTimeout = setTimeout(function() { + var text = searchInput.value; + + if(text == "") { + CrystalDoc.toggleResultsList(false); + }else if(text == lastSearchText){ + document.dispatchEvent(new Event("CrystalDoc:searchDebounceStopped")); + }else{ + CrystalDoc.search(text); + navigator.highlightFirst(); + searchInput.focus(); + } + lastSearchText = text; + setPersistentSearchQuery(text); + }, 200); + }; + + if(location.hash.length > 3 && location.hash.substring(0,3) == "#q="){ + // allows directly linking a search query which is then executed on the client + // this comes handy for establishing a custom browser search engine with https://crystal-lang.org/api/#q=%s as a search URL + // TODO: Add OpenSearch description + var searchQuery = location.hash.substring(3); + history.pushState({searchQuery: searchQuery}, "Search for " + searchQuery, location.href.replace(/#q=.*/, "")); + searchInput.value = searchQuery; + document.addEventListener('CrystalDoc:loaded', performSearch); + } + + if (searchInput.value.length == 0) { + var searchText = sessionStorage.getItem(repositoryName + '::search-input:value'); + if(searchText){ + searchInput.value = searchText; + } + } + searchInput.addEventListener('keyup', performSearch); + searchInput.addEventListener('input', performSearch); + + var usageModal = new UsageModal('Keyboard Shortcuts', '' + + '' + ); + + function handleShortkeys(event) { + var element = event.target || event.srcElement; + + if(element.tagName == "INPUT" || element.tagName == "TEXTAREA" || element.parentElement.tagName == "TEXTAREA"){ + return; + } + + switch(event.key) { + case "?": + usageModal.show(); + break; + + case "Escape": + usageModal.hide(); + break; + + case "s": + case "/": + if(usageModal.isVisible()) { + return; + } + event.stopPropagation(); + navigator.focus(); + performSearch(); + break; + } + } + + document.addEventListener('keyup', handleShortkeys); + + var scrollToEntryFromLocationHash = function() { + var hash = window.location.hash; + if (hash) { + var targetAnchor = unescape(hash.substr(1)); + var targetEl = document.querySelectorAll('.entry-detail[id="' + targetAnchor + '"]'); + + if (targetEl && targetEl.length > 0) { + targetEl[0].offsetParent.scrollTop = targetEl[0].offsetTop; + } + } + }; + window.addEventListener("hashchange", scrollToEntryFromLocationHash, false); + scrollToEntryFromLocationHash(); +}); diff --git a/docs/search-index.js b/docs/search-index.js new file mode 100644 index 0000000..5e09cac --- /dev/null +++ b/docs/search-index.js @@ -0,0 +1 @@ +crystal_doc_search_index_callback({"repository_name":"github.com/lbarasti/statistics","body":"![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\nvar(x, corrected: true) # 21\nvar(x, mean: 8) # 18.0\nstd(x) # 3.7416...\n```\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 ()\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/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/lib/distributions.cr"},{"filename":"statistics.cr","line_number":6,"url":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr"}],"repository_name":"github.com/lbarasti/statistics","program":false,"enum":false,"alias":false,"aliased":"","const":false,"constants":[{"id":"VERSION","name":"VERSION","value":"\"0.1.0\"","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":"

Basic descriptive statistics functionality.

","class_methods":[],"constructors":[],"instance_methods":[{"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":"

Computes several descriptive statistics of the passed array.

","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/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, max: sorted.last, q1: quantile(sorted, 0.25, sorted: true), median: median(sorted, sorted: true), middle: middle(sorted), 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":"

Computes the number of occurrences of each value in the dataset.

","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/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/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":"

Computes the kurtosis of a dataset.

","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 = false, excess = false)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L53","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":"

Computes the mean of a dataset.

","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L72","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":"

Computes the median of all elements in a dataset.

","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 = false)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L86","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":"

Computes the middle of two values a and b.

","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/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L111","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":"

Computes the middle of an array a, which consists of finding its extrema and then computing their mean.

","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":""}],"args_string":"(values)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L105","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":"

Computes the modal (most common) value in a dataset.

","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/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L123","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":"

Calculates the n-th moment about the mean for a sample.

","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 = nil, n = 1)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L134","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":"

Computes the quantile of a dataset at a specified probability p on the interval [0,1].

","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 = false)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L150","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":"

Computes the skewness of a dataset.

","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 = false)","source_link":"https://github.com/lbarasti/statistics/blob/97da7c6c7422ab7208bdbf6822ef57ecd20dec27/src/statistics.cr#L170","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":"

Computes the standard deviation of a dataset.

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