implement shifloNormal

bgctw · Jan 31, 2022 · 4cc9dee · 4cc9dee
1 parent 972c88b
commit 4cc9dee
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diff --git a/Project.toml b/Project.toml
@@ -23,10 +23,3 @@ StatsBase = "0.33"
 StatsFuns = "0.9"
 julia = "1.6"
 
-[extras]
-Optim = "429524aa-4258-5aef-a3af-852621145aeb"
-Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[targets]
-test = ["Test", "Random", "Optim"]
diff --git a/docs/Project.toml b/docs/Project.toml
@@ -1,5 +1,4 @@
 [deps]
-DistributionFits = "45214091-1ed4-4409-9bcf-fdb48a05e921"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"

diff --git a/docs/src/logitnormal.md b/docs/src/logitnormal.md
@@ -59,5 +59,13 @@ end
 p # hide
 ```
 
+A shifted and scaled version of this distribution can be
+used as a moother alternative to the Bounded uniform distribution.
+
+```@docs
+shifloNormal
+```
+
+
 
 
diff --git a/inst/flat.jl b/inst/flat.jl
@@ -0,0 +1,39 @@
+# determine the steepest part of the most spread flat logitnorm
+
+using Optim
+using StatsFuns
+using DistributionFits
+using StatsPlots
+
+dln = fit_mode_flat(LogitNormal, 0.5)
+
+# Sympy
+# x = symbols('x', nonnegative=True, real=True)
+# lx = ln(x/(1-x))
+# lnormx = 1/(2*sqrt(2*pi)) * 1/(x*(1-x)) * exp(-1/4*lx*lx)
+# dlnormx = simplify(diff(lnormx,x))
+# ddlnormx = simplify(diff(dlnormx,x))
+# ccode(dlnormx)
+
+# second derivative via sympy
+pow(b,e) = b^e
+ddlogit(x) = −1.0/16.0*sqrt(2)*(24*pow(x,2)−12*x*log(−x/(x−1))−24*x+pow(log(−x/(x−1)),2)+6*log(−x/(x−1))+6)*exp(−1.0/4.0*pow(log(−x/(x−1)),2))/(sqrt(pi)*pow(x,3)*(pow(x,3)−3*pow(x,2)+3*x−1))
+
+# first derivative via numpy
+dlogit(x) = (1.0/8.0)*sqrt(2)*(4*x−log(−x/(x−1))−2)*exp(−1.0/4.0*pow(log(−x/(x−1)),2))/(sqrt(pi)*pow(x,2)*pow(x−1,2))
+
+
+ansopt2 = optimize(dlogit, 0.9, 1)
+ansopt2
+xms = ansopt2.minimizer
+
+x = 0.7:0.002:1.0
+x = x[1:(end-1)]
+plot(x, dlogit.(x))
+vline!([xms])
+
+plot(x, pdf.(dln,x))
+vline!([xms])
+
+
+
diff --git a/src/DistributionFits.jl b/src/DistributionFits.jl
@@ -24,7 +24,7 @@ export
 export AbstractΣstar, Σstar, σstar
 
 # LogitNormal  
-export fit_mode_flat
+export fit_mode_flat, shifloNormal
 
 # dependency inversion: need to define DistributionFits.optimize by user
 export AbstractDistributionFitOptimizer, optimize

diff --git a/src/univariate/continuous/logitnormal.jl b/src/univariate/continuous/logitnormal.jl
@@ -127,6 +127,19 @@ function of_mode_flat(x, m, logitm = logit(m))
   d*d
 end
 
+"""
+    shifloNormal(lower,upper)
+
+Get a Shifted Flat LogitNormal distribution that is most spread
+with an extent between lower and upper. 
+This is a more smooth alternative to the bounded uniform distribution.
+"""
+function shifloNormal(lower,upper)
+    lower,upper = promote(lower,upper/1)
+    dln = LogitNormal{typeof(lower)}(0.0, sqrt(2))
+    LocationScale(lower, (upper -lower), dln)
+end
+
 
 
 

diff --git a/src/univariate/continuous/lognormal.jl b/src/univariate/continuous/lognormal.jl
@@ -115,3 +115,5 @@ function fit(::Type{LogNormal}, mean, σstar::AbstractΣstar)
     LogNormal(μ, σ)
 end
 
+
+
Original file line number	Diff line number	Diff line change
Expand Up		@@ -115,3 +115,5 @@ function fit(::Type{LogNormal}, mean, σstar::AbstractΣstar)
		LogNormal(μ, σ)
		end