ENH: more inverses for distribution CDFs

[dschmitz89]

Over at scipy/scipy#23308 I implemented the inverse of the noncentral F distibution CDF with respect to the noncentrality parameter (the legacy cdflib library called this ncfdtrinc) using boost. It is a straight forward exercise for bracket_and_solve_root and works well.

Now my question is if such inverses are of interest for boost.math itself? For the noncentral chi squared distribution, these inverses are for example implemented. Such functions have statistical applications (see for example here in statsmodels).

[mborland]

We will certainly take it if you are offering. I can review your code here or there if need be, just let me know.

[dschmitz89]

I had a look at the noncentral chi squared code, that looks almost reasonable to deal with for a non veteran C++ developer. What is more intimidating is how to setup the environment and create test cases. If I understand correctly, you use boost.multiprecision for that purpose. Do you have detailed docs somewhere?

I will try to get to that in future but for the time being, if you have time to help out with the review in scipy that would be highly appreciated.

[mborland]

The distributions are in general tested against float, double, and long double with spot values calculated by Mathematica (and others). There's also a type called real_concept which emulates a multi-precision type, but is in practice a wrapper around a long double. I don't think there's any real documentation on the testing harness for the distributions. In your case the only types of concern are float and double right?

[dschmitz89]

Yep, float and double are all we need in scipy. Your testing mechanism do not seem to be so different from scipy. There we mostly rely on spot checks using some high precision references as well.

[jzmaddock]

Note that we already have test data, it's just that if you use it in reverse (to compute non-centrality) then there may be some ill-conditioned inputs lurking in there. If you look at the existing tests for the inverses, you'll see me filtering those out.

[dschmitz89]

To be more specific, the list of distributions for which we would like to implement the inverses of the CDF with respect to its other parameters (quantiles already exist) are:

• noncentral F
• noncentral t
• fisher_f (regular F distribution)
• Student t

If you are interested in all those, we can start in the coming months.

[mborland]

That would be great. If you want to merge a simplified version into scipy before boost you can ping me to review.