Add docs distributions

FSharp.Stats.sln

@@ -28,10 +28,12 @@ Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "tools", "tools", "{83F16175
 EndProject
 Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "content", "content", "{8E6D5255-776D-4B61-85F9-73C37AA1FB9A}"
 	ProjectSection(SolutionItems) = preProject
+		docs\content\Distributions.fsx = docs\content\Distributions.fsx
 		docs\content\index.fsx = docs\content\index.fsx
 		docs\content\Matrix_Vector.fsx = docs\content\Matrix_Vector.fsx
 		docs\content\Optimization.fsx = docs\content\Optimization.fsx
 		docs\content\SpecialFunctions.fsx = docs\content\SpecialFunctions.fsx
+		docs\content\Testing.fsx = docs\content\Testing.fsx
 		docs\content\tutorial.fsx = docs\content\tutorial.fsx
 	EndProjectSection
 EndProject

docs/content/Distributions.fsx

@@ -0,0 +1,64 @@
+(*** hide ***)
+// This block of code is omitted in the generated HTML documentation. Use 
+// it to define helpers that you do not want to show in the documentation.
+#I "../../bin"
+#r "../../packages/build/FSharp.Plotly/lib/net40/Fsharp.Plotly.dll"
+open FSharp.Plotly
+(**
+Probability Distributions
+=========================
+
+FSharp.Stats a provides a wide range of probability distributions. Given the
+distribution parameters they can be used to investigate their statistical properties
+or to sample non-uniform random numbers.
+
+*)
+#r "FSharp.Stats.dll"
+open FSharp.Stats
+open FSharp.Stats.Distributions
+
+
+// https://en.wikipedia.org/wiki/Student%27s_t-distribution
+let tmp = 
+    Seq.init 100
+        (fun _ -> Continuous.StudentT.Sample 1. 1. 1.)
+    |> Empirical.create 0.1
+
+
+
+
+let studentTParams = [(1.,1.,1.);(1.,1.,2.);(1.,1.,5.);]
+let xStudentT = [-4. ..0.1.. 4.]
+
+let pdfStudentT mu tau dof = 
+    xStudentT 
+    |> List.map (Continuous.StudentT.PDF mu tau dof)
+    |> List.zip xStudentT
+
+studentTParams
+|> List.map (fun (mu,tau,dof) -> Chart.Spline(pdfStudentT mu tau dof,Name=sprintf "mu=%.1f tau=%.1f dof=%.1f" mu tau dof,ShowMarkers=false))
+(*** define-output:PdfStudentT ***)
+|> Chart.Combine
+|> Chart.withX_AxisStyle("x",MinMax=(-4.,4.))
+|> Chart.withY_AxisStyle("P(x)",MinMax=(0.,0.4))
+|> Chart.withSize (500., 450.)
+(*** include-it:PdfStudentT ***)
+|> Chart.Show
+
+
+let cdfStudentT mu tau dof = 
+    xStudentT 
+    |> List.map (Continuous.StudentT.CDF  mu tau dof)
+    |> List.zip xStudentT
+
+studentTParams
+|> List.map (fun (mu,tau,dof) -> Chart.Spline(cdfStudentT mu tau dof,Name=sprintf "mu=%.1f tau=%.1f dof=%.1f" mu tau dof,ShowMarkers=false))
+(*** define-output:CdfStudentT ***)
+|> Chart.Combine
+|> Chart.withX_AxisStyle("x",MinMax=(-4.,4.))
+|> Chart.withY_AxisStyle("P(x)",MinMax=(0.,1.))
+|> Chart.withSize (500., 450.)
+(*** include-it:CdfStudentT ***)
+|> Chart.Show
+
+

docs/content/Testing.fsx

@@ -0,0 +1,19 @@
+(*** hide ***)
+// This block of code is omitted in the generated HTML documentation. Use 
+// it to define helpers that you do not want to show in the documentation.
+#I "../../bin"
+#r "../../packages/build/FSharp.Plotly/lib/net40/Fsharp.Plotly.dll"
+open FSharp.Plotly
+(**
+Statistical testing
+===================
+
+FSharp.Stats a provides 
+A hypothesis test is a statistical test that is used to determine whether there is enough evidence 
+in a sample of data to infer that a certain condition is true for the entire population. 
+A hypothesis test examines two opposing hypotheses about a population: the null hypothesis and the alternative hypothesis.
+
+
+*)
+#r "FSharp.Stats.dll"
+open FSharp.Stats

docs/content/index.fsx

@@ -5,63 +5,33 @@
 
 (**
 FSharp.Stats
-======================
+============
 
-Documentation
+FSharp.Stats aims to be a user-friendly library for numerical and statistical computation written in F#.
 
-<div class="row">
-  <div class="span1"></div>
-  <div class="span6">
-    <div class="well well-small" id="nuget">
-      The FSharp.Stats library can be <a href="https://nuget.org/packages/FSharp.Stats">installed from NuGet</a>:
-      <pre>PM> Install-Package FSharp.Stats</pre>
-    </div>
-  </div>
-  <div class="span1"></div>
-</div>
 
 Example
 -------
 
-This example demonstrates using a function defined in this sample library.
+This example demonstrates using a function defined in FSharp.Stats library.
 
 *)
 #r "FSharp.Stats.dll"
 open FSharp.Stats
 
-printfn "hello = %i" <| Library.hello 0
 
-(**
-Some more info
-
-Samples & documentation
------------------------
+// let A = 
+//     matrix [ [ 1.0; 7.0; 2.0 ]
+//              [ 1.0; 3.0; 1.0 ]
+//              [ 2.0; 9.0; 1.0 ] ]
 
-The library comes with comprehensible documentation. 
-It can include tutorials automatically generated from `*.fsx` files in [the content folder][content]. 
-The API reference is automatically generated from Markdown comments in the library implementation.
+// let B = 
+//     matrix [ [ 10.0; 70.0; 20.0 ]
+//              [ 10.0; 30.0; 10.0 ]
+//              [ 20.0; 90.0; 10.0 ] ]
 
- * [Tutorial](tutorial.html) contains a further explanation of this sample library.
 
- * [API Reference](reference/index.html) contains automatically generated documentation for all types, modules
-   and functions in the library. This includes additional brief samples on using most of the
-   functions.
- 
-Contributing and copyright
---------------------------
+// let v = 
+//     vector [|2.0; 20.0; 1.|]
 
-The project is hosted on [GitHub][gh] where you can [report issues][issues], fork 
-the project and submit pull requests. If you're adding a new public API, please also 
-consider adding [samples][content] that can be turned into a documentation. You might
-also want to read the [library design notes][readme] to understand how it works.
 
-The library is available under Public Domain license, which allows modification and 
-redistribution for both commercial and non-commercial purposes. For more information see the 
-[License file][license] in the GitHub repository. 
-
-  [content]: https://github.com/fsprojects/FSharp.Stats/tree/master/docs/content
-  [gh]: https://github.com/fsprojects/FSharp.Stats
-  [issues]: https://github.com/fsprojects/FSharp.Stats/issues
-  [readme]: https://github.com/fsprojects/FSharp.Stats/blob/master/README.md
-  [license]: https://github.com/fsprojects/FSharp.Stats/blob/master/LICENSE.txt
-*)

src/FSharp.Stats/Distributions/Continuous.fs

@@ -545,7 +545,6 @@ module Continuous =
         /// Computes the cumulative distribution function.
         static member CDF mu tau dof x =
             studentTCheckParam mu tau dof            
-            failwith "Not implemented yet."
             let k = (x - mu) / tau
             let h = dof / (dof + (k * k))
             let ib = 0.5 * SpecialFunctions.Beta.lowerIncomplete (dof/2.0) 0.5 h