Add Wilcoxon Distribution

[bvenn]

Description

The signed rank test currently is only an approximation for large values (see https://github.com/fslaborg/FSharp.Stats/pull/182#discussion_r908169551) There is a valid wilcoxon distribution that is quite expensive to calculate. Nevertheless it is required to calculate exact u test results, and should be implemented:

Citation from #213

To perform a valid u test it is required to implement the Wilcoxon distribution. Is should be added as individual source file within Distributions/Continuous. You can copy the Distributions/Continuous/Normal.fs and replace all fields with its corresponding entries for the Wilcoxon distribution.

References

• [1] Rwilcox
• [2] R vigenette
• [3] analytica wilcox
• [4] original publication

Pointers

• suggested workflow:
  • check out other distribution implementations and the original publication
  • copy a existing source file (e.g. Normal.fs), rename it to Wilcoxon.fs and replace all members.
    • this may be harder as you would imagine, but even if not all members are implemented, it would help us bringing FSharp.Stats a step further
  • optional: add unit tests

Hints (click to expand if you need additional pointers)

A final PR should contain the source file as well as unit tests to verify the correct results of the calculations. But even if some functions are missing, you can file a PR and mention what has to be added and where the problems are. For appropriate unit tests you can check out [exponential distribution unit tests](https://github.com/fslaborg/FSharp.Stats/blob/8fb5d6dd07ff213a4e91b618fb2e654bc6147985/tests/FSharp.Stats.Tests/DistributionsContinuous.fs#L1064). - 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](https://dotnet.microsoft.com/en-us/download) - to build the binaries yourself follow the [instructions](https://fslab.org/FSharp.Stats/#Installation) - while working on the [FSharp.Stats documentation](https://fslab.org/FSharp.Stats/) (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'll take a stab at that.

[valbers]

Ok. @bvenn , like we discsussed, it seems like this requirement needs some refinement, since this distribution was already there once and got removed ( https://github.com/fslaborg/FSharp.Stats/issues/213 ), so I'm leaving it at it for now.