add variance functions

FStats/AssemblyInfo.fs

@@ -11,6 +11,6 @@ module AssemblyInfo =
     [<AssemblyFileVersion("1.0.0.0")>]
     [<AssemblyProduct("FStats")>]
     [<AssemblyTitle("FStats")>]
-    [<AssemblyVersion("0.1.6.0")>]
+    [<AssemblyVersion("0.1.8.0")>]
 
     do ()

FStats/DescriptiveStatistics.fs

@@ -18,8 +18,10 @@ module DescriptiveStatistics =
             Median             = median data
             Minimum            = minimum
             Mode               = mode data
+            PopulationVariance = populationVariance data
             Range              = maximum - minimum
             UpperQuartile      = upperQuartile
+            Variance           = variance data
         }
 
 

FStats/Script.fsx

@@ -12,6 +12,10 @@ let data =
 
 let stats = DescriptiveStatistics.describe data
 
+let interQuartileRange   = stats.InterQuartileRange
+let interQuartileRange'  = Statistics.interQuartileRange data
+let interQuartileRange'' = Seq.interQuartileRange data
+
 let q1 = stats.LowerQuartile
 let q1' = Statistics.lowerQuartile data
 let q1'' = Seq.lowerQuartile data
@@ -36,10 +40,18 @@ let mode   = stats.Mode
 let mode'  = Statistics.mode data
 let mode'' = Seq.mode data
 
+let popVariance   = stats.PopulationVariance
+let popVariance'  = Statistics.populationVariance data
+let popVariance'' = Seq.populationVariance data
+
 let range   = stats.Range
 let range'  = Statistics.range data
 let range'' = Seq.range data
 
 let q3   = stats.UpperQuartile
 let q3'  = Statistics.upperQuartile data
 let q3'' = Seq.upperQuartile data
+
+let variance   = stats.Variance
+let variance'  = Statistics.variance data
+let variance'' = Seq.variance data

FStats/Seq.fs

@@ -8,6 +8,8 @@ module Seq =
     let mean               = Statistics.mean
     let median             = Statistics.median
     let minimum            = Statistics.minimum
-    let mode               = Statistics.mode        
+    let mode               = Statistics.mode
+    let populationVariance = Statistics.populationVariance     
     let range              = Statistics.range
     let upperQuartile      = Statistics.upperQuartile
+    let variance           = Statistics.variance

FStats/Statistics.fs

@@ -67,6 +67,16 @@ module Statistics =
         |> Seq.map fst
         |> Seq.toList
 
+    /// <summary>Calculates the variance of a data set using N degrees of freedom.</summary>
+    /// <param name="data">The dat set.</param>
+    /// <returns>The variance value.</returns>
+    let inline populationVariance (data: seq<float>) =
+        let mean = mean data
+        data
+        |> Seq.map (fun x -> pown x 2)
+        |> Seq.average
+        |> (fun x -> x - (pown mean 2))
+
     /// <summary>Calculates the range of a data set.</summary>
     /// <param name="data">The dat set.</param>
     /// <returns>The range value.</returns>
@@ -84,3 +94,13 @@ module Statistics =
         let isEven = float (Seq.length data * 3) / 4. |> (fun x -> x % 2. = 0.)
         patternMatch isEven index sortedData
 
+    /// <summary>Calculates the variance of a data set using (N - 1) degrees of freedom.</summary>
+    /// <param name="data">The dat set.</param>
+    /// <returns>The variance value.</returns>
+    let inline variance (data: seq<float>) =
+        let mean = mean data
+        data
+        |> Seq.map (fun x -> pown x 2)
+        |> Seq.sum
+        |> (fun x -> x / (Seq.length data - 1 |> float))
+        |> (fun x -> x - (pown mean 2))

FStats/Types.fs

@@ -11,8 +11,10 @@ module Types =
             Median             : float
             Minimum            : float
             Mode               : float list
+            PopulationVariance : float
             Range              : float
             UpperQuartile      : float
+            Variance           : float
         }