add confidence interval calculation

#74

src/FSharp.Stats/ConfidenceInterval.fs

@@ -0,0 +1,19 @@
+namespace FSharp.Stats
+
+module ConfidenceInterval =
+
+    open FSharp.Stats.Distributions
+
+    // The deviation from the sample mean is calculated by using a t distribution. Common ciLevel = 0.95
+    let ciDeviation ciLevel (sample : seq<float>)=
+        let n = float (Seq.length sample)
+        let stDev = Seq.stDev sample
+        let t = Continuous.getCriticalTValue (float n - 1.) (1. - ciLevel) Continuous.TwoTailed
+        let delta = t * stDev / sqrt (float n)
+        delta
+
+    // The confidence interval is calculated by using a t distribution. Common ciLevel = 0.95
+    let ci ciLevel (sample : seq<float>)=
+        let mean  = Seq.mean  sample
+        let delta = ciDeviation ciLevel sample
+        Intervals.create (mean - delta) (mean + delta)

src/FSharp.Stats/FSharp.Stats.fsproj

@@ -104,8 +104,8 @@
     <Compile Include="Testing\SAM.fs" />
     <Compile Include="Testing\FisherHotelling.fs" />
     <Compile Include="Testing\RMT.fs" />
-    <Compile Include="Fitting\CrossValidation.fs" />
     <!-- Fitting -->
+    <Compile Include="Fitting\CrossValidation.fs" />
     <Compile Include="Fitting\LinearRegression.fs" />
     <Compile Include="Fitting\NonLinearRegression.fs" />
     <Compile Include="Fitting\GoodnessOfFit.fs" />
@@ -125,6 +125,7 @@
     <Compile Include="ML\Unsupervised\GapStatistics.fs" />
     <!-- MISC -->
     <Compile Include="FSIPrinters.fs" />
+    <Compile Include="ConfidenceInterval.fs" />
     <None Include="paket.references" />
     <None Include="paket.template" />
   </ItemGroup>