From 68d724a008b9b0f27dfa21a99c4d62b52caf630b Mon Sep 17 00:00:00 2001
From: omaus <omaus@bio.uni-kl.de>
Date: Wed, 26 Jan 2022 23:22:38 +0100
Subject: [PATCH 1/2] Add Kolmogorov-Smirnov test :construction:

---
 src/FSharp.Stats/FSharp.Stats.fsproj          |  1 +
 src/FSharp.Stats/Testing/KolmogorovSmirnov.fs | 44 +++++++++++++++++++
 2 files changed, 45 insertions(+)
 create mode 100644 src/FSharp.Stats/Testing/KolmogorovSmirnov.fs

diff --git a/src/FSharp.Stats/FSharp.Stats.fsproj b/src/FSharp.Stats/FSharp.Stats.fsproj
index fd456944..d6271959 100644
--- a/src/FSharp.Stats/FSharp.Stats.fsproj
+++ b/src/FSharp.Stats/FSharp.Stats.fsproj
@@ -115,6 +115,7 @@
     <Compile Include="Testing\FTest.fs" />
     <Compile Include="Testing\FriedmanTest.fs" />
     <Compile Include="Testing\HTest.fs" />
+    <Compile Include="Testing\KolmogorovSmirnov.fs" />
     <Compile Include="Testing\ChiSquareTest.fs" />
     <Compile Include="Testing\Bartlett.fs" />
     <Compile Include="Testing\PostHoc.fs" />
diff --git a/src/FSharp.Stats/Testing/KolmogorovSmirnov.fs b/src/FSharp.Stats/Testing/KolmogorovSmirnov.fs
new file mode 100644
index 00000000..2316bbaa
--- /dev/null
+++ b/src/FSharp.Stats/Testing/KolmogorovSmirnov.fs
@@ -0,0 +1,44 @@
+namespace FSharp.Stats.Testing
+
+open FSharp.Stats.Distributions
+
+module KolmogorovSmirnov =
+    
+    /// Tests the input values with the Kolmogorov-Smirnov Goodness of Fit-test against a normal distribution and returns a p-Value. 
+    /// The p-value indicates how likely it is to observe such a distribution under the assumption that the null hypothesis is true (= sample distribution normally distributed).  
+    /// In short: The lower the p-value, the more likely it is that the sample does NOT originate from a normal distribution.
+    let goF values =
+        let lVals = Array.length values |> float
+        let rankedVals = Array.sort values
+        let rankedNormVals = rankedVals |> Array.mapi (fun i _ -> float i / lVals)
+        let meanVals = FSharp.Stats.Seq.mean values
+        let stdVals = FSharp.Stats.Seq.stDev values
+        let nD = FSharp.Stats.Distributions.Continuous.normal meanVals stdVals
+        let cum = rankedVals |> Array.map (fun v -> nD.CDF v)
+        let deltaCumVals = (cum, rankedNormVals) ||> Array.map2 (fun c v -> System.Math.Abs (c - v))
+        let kS = Array.max deltaCumVals
+        kS
+        //Continuous.kolmogorov 
+        // let z = kS * (System.Math.Sqrt())
+        // let kolmoDist x = (System.Math.Sqrt (2. * System.Math.PI) / x) * 
+
+module Distributions =
+    
+    // TO DO
+    let cdfKolmogorov x =
+        let fraction = (System.Math.Sqrt(2. * System.Math.PI)) / x
+        printfn "fraction: %f" fraction
+        let eFractionDenominator = 8. * x ** 2.
+        printfn "eFractionDenominator: %f" eFractionDenominator
+        let rec getSum acc k n =
+            printfn "k: %f" k
+            let eFractionNumerator = -(2. * k - 1.) ** 2. * System.Math.PI ** 2.
+            printfn "eFractionNumerator: %f" eFractionNumerator
+            let newAcc = acc + System.Math.E ** (eFractionNumerator / eFractionDenominator)
+            printfn "newAcc: %f" newAcc
+            if k < n then getSum newAcc (k + 1.) n
+            else newAcc
+        let sum = getSum 0. 1. 1.
+        fraction * sum
+    
+    //cdfKolmogorov 1.3581
\ No newline at end of file

From cfc6958b121eb50db609f6ebb5dac0543f014483 Mon Sep 17 00:00:00 2001
From: omaus <omaus@bio.uni-kl.de>
Date: Fri, 28 Jan 2022 11:44:20 +0100
Subject: [PATCH 2/2] Delete unused/not-working distribution :fire:

---
 src/FSharp.Stats/Testing/KolmogorovSmirnov.fs | 25 +------------------
 1 file changed, 1 insertion(+), 24 deletions(-)

diff --git a/src/FSharp.Stats/Testing/KolmogorovSmirnov.fs b/src/FSharp.Stats/Testing/KolmogorovSmirnov.fs
index 2316bbaa..34369635 100644
--- a/src/FSharp.Stats/Testing/KolmogorovSmirnov.fs
+++ b/src/FSharp.Stats/Testing/KolmogorovSmirnov.fs
@@ -18,27 +18,4 @@ module KolmogorovSmirnov =
         let deltaCumVals = (cum, rankedNormVals) ||> Array.map2 (fun c v -> System.Math.Abs (c - v))
         let kS = Array.max deltaCumVals
         kS
-        //Continuous.kolmogorov 
-        // let z = kS * (System.Math.Sqrt())
-        // let kolmoDist x = (System.Math.Sqrt (2. * System.Math.PI) / x) * 
-
-module Distributions =
-    
-    // TO DO
-    let cdfKolmogorov x =
-        let fraction = (System.Math.Sqrt(2. * System.Math.PI)) / x
-        printfn "fraction: %f" fraction
-        let eFractionDenominator = 8. * x ** 2.
-        printfn "eFractionDenominator: %f" eFractionDenominator
-        let rec getSum acc k n =
-            printfn "k: %f" k
-            let eFractionNumerator = -(2. * k - 1.) ** 2. * System.Math.PI ** 2.
-            printfn "eFractionNumerator: %f" eFractionNumerator
-            let newAcc = acc + System.Math.E ** (eFractionNumerator / eFractionDenominator)
-            printfn "newAcc: %f" newAcc
-            if k < n then getSum newAcc (k + 1.) n
-            else newAcc
-        let sum = getSum 0. 1. 1.
-        fraction * sum
-    
-    //cdfKolmogorov 1.3581
\ No newline at end of file
+        Continuous.kolmogorov 
\ No newline at end of file