Update Support member for all probability distributions

[bvenn]

Description

The syntax for the static member Support [within distributions] are written in a different syntax.
@Freymaurer in #222

The Support of distributions defines the range of values the parameter can take. At the moment, there is a mixture of types for the Support. It is either defined as tuple, Interval, or undefined. To homogenize all distribution fields, it is required to change all tuple supports to Interval<float> or Interval<int> like it is done here:

FSharp.Stats/src/FSharp.Stats/Distributions/Discrete/Binomial.fs

Lines 120 to 122 in 8fb5d6d

	static member Support p n =
	Binomial.CheckParam p n
	Interval.CreateClosed<int> (0,n)

Please check the validity of each existing distribution-support and create the appropriate Interval that either is of type Interval<float> or Interval<int> for discrete distributions. The Wikipedia pages for probability distributions are a great source to verify the correct support (e.g. on the right side of Chi squared distribution).

There may be distributions where no support can be defined or it is not clear on first sight. Please comment these cases here!

References

• [1] [Feature Request] Unify Support syntax for all Distributions #222
• [2] wikipedia pages of each probability distribution

Pointers

• Interval types:

  open FSharp.Stats
  Interval.CreateClosed(2.,3.)    // corresponds to [2.0,3.0] 2 and 3 are included
  Interval.CreateOpen(2.,3.)      // corresponds to (2.0,3.0) 2 and 3 are excluded
  Interval.CreateLeftOpen(2.,3.)  // corresponds to (2.0,3.0] 2 is excluded, 3 is included
  Interval.CreateRightOpen(2.,3.) // corresponds to [2.0,3.0) 2 is included, 3 is excluded

• suggested workflow:
  • find a distribution where the support field is missing or is of type (a,b). A list is given below!
  • research the correct support for the distribution and compare it with the existing one
  • update (a,b) to either Interval.CreateClosed(a,b) or Interval.CreateLeftOpen(a,b)

Hints (click to expand if you need additional pointers)

• FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/Beta.fs

  Line 129 in 8fb5d6d

  static member Support alpha beta =

• FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/Chi.fs

  Line 76 in 8fb5d6d

  static member Support dof =

• FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/F.fs

  Line 103 in 8fb5d6d

  static member Support dof1 dof2 =

• FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/Gamma.fs

  Line 166 in 8fb5d6d

  (0.0, System.Double.PositiveInfinity)

• FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/LogNormal.fs

  Line 76 in 8fb5d6d

  static member Support mu sigma =

• https://github.com/fslaborg/FSharp.Stats/blob/developer/src/FSharp.Stats/Distributions/Continuous/MultivariateNormal.fs

• FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/Normal.fs

  Line 132 in 8fb5d6d

  (System.Double.NegativeInfinity, System.Double.PositiveInfinity)

• FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/StudentT.fs

  Line 78 in 8fb5d6d

  (System.Double.NegativeInfinity, System.Double.PositiveInfinity)

• StudentizedRange distribution

• MultivariateNormal distribution

• check for correct interval type!

  FSharp.Stats/src/FSharp.Stats/Distributions/Continuous/Exponential.fs

  Line 91 in 8fb5d6d

  static member Support lambda =

• To be able to contribute to this library you'll need

  • an GitHub account
  • an IDE like Visual Studio Community or Visual Studio Code
  • dotnet 6 sdk

• to build the binaries yourself follow the instructions

• while working on the FSharp.Stats documentation (any file within https://github.com/fslaborg/FSharp.Stats/tree/developer/docs) you can navigate to the project folder with a prompt of your choice and use the command ./build watchdocs

• unit tests can be executed via ./build runtests

[valbers]

I'm going to take a look at that.

[valbers]

--> #301