ENH: stats: adding more random number generators from UNU.RAN

UNU.RAN contains many generators to sample from univariate continuous and discrete distributions. gh-14215 adds two such generators TransformedDensityRejection and DiscreteAliasUrn. Over time it would be great to add these generators to SciPy:

For continuous distributions:

• NumericalInversePolynomial (#14619)
• NumericalInverseHermite (#14703)
• NumericalInversion
• AutomaticRatioUniforms
• NaiveRatioUniforms
• SimpleRatioUniforms (#15142)
• AdaptiveRejectionSampling
• InverseTransformedDensityRejection
• SimpleSetupRejection
• TransformedDensityRejection (#14215)
• UniversalTransformedDensityRejection
• PiecewiseConstantHatsTable

For discrete distributions:

• DiscreteAutomaticRejectionInversion
• DiscreteAliasUrn (#14215)
• DiscreteGuideTable (#14828)
• DiscreteSimpleRatioOfUniforms
• DiscreteSequentialSearch

More details of all these generators can be found in this spreadsheet.

Updated 25 October: some methods do not need to be added to SciPy, see https://github.com/scipy/scipy/issues/14600#issuecomment-951174964

[chrisb83]

@Kai-Striega It would be great if you help us!

gh-14717 should give a good overview of the required code changes to add a new method. Both Tirth and I noted that writing the docs / tutorial takes up most of the time (though one can copy quite a few things from UNU.RAN).

Tirth will soon work on SimpleRatioUniforms and I will implement AutomaticRatioUniforms. You can take a look at any of the other methods. I think DiscreteGuideTable would be nice to add (https://statmath.wu.ac.at/unuran/doc/unuran.html#DGT)

Let us know if you would like to have a virtual meeting to discuss this in more detail

[chrisb83]

I will close this issue since we do not plan to add further methods for now