From 4cc9dee45f38b97bfada89832789bb965884d7cc Mon Sep 17 00:00:00 2001
From: Thomas Wutzler <twutz@bgc-jena.mpg.de>
Date: Mon, 31 Jan 2022 16:45:36 +0100
Subject: [PATCH] implement shifloNormal

---
 Project.toml                             |   7 -
 docs/Project.toml                        |   1 -
 docs/src/logitnormal.md                  |   8 +
 inst/flat.jl                             |  39 +++
 src/DistributionFits.jl                  |   2 +-
 src/univariate/continuous/logitnormal.jl |  13 +
 src/univariate/continuous/lognormal.jl   |   2 +
 test/Manifest.toml                       | 426 +++++++++++++++++++++++
 test/Project.toml                        |   7 +
 test/logitnormal.jl                      |  10 +
 10 files changed, 506 insertions(+), 9 deletions(-)
 create mode 100644 inst/flat.jl
 create mode 100644 test/Manifest.toml
 create mode 100644 test/Project.toml

diff --git a/Project.toml b/Project.toml
index 517743c..809ddc8 100644
--- 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
index c568697..5e0a9e7 100644
--- 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
index 7d159c0..a755bd6 100644
--- 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
new file mode 100644
index 0000000..a536f5a
--- /dev/null
+++ 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
index 1f340d2..26a1733 100644
--- 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
index dc61054..1178820 100644
--- 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
index 4749731..51726f8 100644
--- 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
 
+
+
diff --git a/test/Manifest.toml b/test/Manifest.toml
new file mode 100644
index 0000000..c8b0c3a
--- /dev/null
+++ b/test/Manifest.toml
@@ -0,0 +1,426 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.7.1"
+manifest_format = "2.0"
+
+[[deps.ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
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+uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
+
+[[deps.Sockets]]
+uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
+
+[[deps.SortingAlgorithms]]
+deps = ["DataStructures"]
+git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "1.0.1"
+
+[[deps.SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[deps.SpecialFunctions]]
+deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
+git-tree-sha1 = "e6bf188613555c78062842777b116905a9f9dd49"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+version = "2.1.0"
+
+[[deps.Static]]
+deps = ["IfElse"]
+git-tree-sha1 = "b4912cd034cdf968e06ca5f943bb54b17b97793a"
+uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
+version = "0.5.1"
+
+[[deps.StaticArrays]]
+deps = ["LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "2884859916598f974858ff01df7dfc6c708dd895"
+uuid = "90137ffa-7385-5640-81b9-e52037218182"
+version = "1.3.3"
+
+[[deps.Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[deps.StatsAPI]]
+git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
+version = "1.2.0"
+
+[[deps.StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.33.14"
+
+[[deps.StatsFuns]]
+deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "f35e1879a71cca95f4826a14cdbf0b9e253ed918"
+uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+version = "0.9.15"
+
+[[deps.SuiteSparse]]
+deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
+uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+
+[[deps.TOML]]
+deps = ["Dates"]
+uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
+
+[[deps.Tar]]
+deps = ["ArgTools", "SHA"]
+uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
+
+[[deps.Test]]
+deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
+uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[deps.UUIDs]]
+deps = ["Random", "SHA"]
+uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
+
+[[deps.UnPack]]
+git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
+uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
+version = "1.0.2"
+
+[[deps.Unicode]]
+uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+
+[[deps.Zlib_jll]]
+deps = ["Libdl"]
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+
+[[deps.nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+
+[[deps.p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
diff --git a/test/Project.toml b/test/Project.toml
new file mode 100644
index 0000000..79d3ec0
--- /dev/null
+++ b/test/Project.toml
@@ -0,0 +1,7 @@
+[deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+Optim = "429524aa-4258-5aef-a3af-852621145aeb"
+QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/test/logitnormal.jl b/test/logitnormal.jl
index 7682ead..7045642 100644
--- a/test/logitnormal.jl
+++ b/test/logitnormal.jl
@@ -111,3 +111,13 @@ end
     #plot(d1)
 end
 
+@testset "shifloNormal" begin
+    d = shifloNormal(1,3)
+    @test isapprox(mode(d), 2.0, atol=0.001)
+    @test minimum(d) == 1.0
+    @test maximum(d) == 3.0
+    @test scale(d) == 3-1
+    @test location(d) == 1.0
+    #plot(d)
+end;
+