boostorg / boostorg/math

New special functions: logarithm of incomplete gamma and beta functions

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Description

The incomplete gamma and beta functions arise in a LOT of cumulative density functions. Very accurate implementations of them are quite common and also in Boost. What I have not seen yet are implementations of their logarithms. These would be very helpful to compute accurate logarithms of CDF and SFs. One example is an issue in SciPy where a user wants to compute the logcdf of the Poisson distribution for not even very extreme values: https://github.com/scipy/scipy/issues/8424. Here the logarithm of the incomplete regularized gamma function would come very much in handy.

SciPy includes the logarithm of the normal distribution CDF [already](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.log_ndtr.html) but incomplete beta and gamma functions are of course a larger beast to kill.

Is this something you would find worthwile for Boost?

Edit: CC ing the special function wizards @steppi @WarrenWeckesser

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Research direction

No file or test is named. Start by reviewing Boost.Math's existing incomplete gamma and beta special functions, then read the referenced SciPy logcdf issue for motivation and expected use cases. Done means the logarithms of the incomplete gamma and beta functions are implemented with demonstrated numerical accuracy.

Written by the indexing model from the issue text.

Assessment

Tech stack
cpp
Domain
backend
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
30/100

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