Initial implementation of find_non_centrality for non_central_f_distribution

[JacobHass8]

See #1305 for for details.

[JacobHass8]

@dschmitz89 how does this first commit look in regards to #1338 (comment)

[dschmitz89]

Thanks @JacobHass8 for looking into this so quickly. This is a good start. I am not a boost maintainer (barely a boost developer), so can only comment from a high level.

The most important missing bit here is tests for the new functionality. I could not find the current noncentral F distribution tests after 2 minutes though, so we will have to rely on the boost devs to guide us a little here.

[jzmaddock]

Yup, tests needed.

Non central F is treated as a special case of the non-central beta (which is where most of the tests are). Non-central F tests are fairly lightweight, just there to make sure we have the transformation to non-central beta correct really: https://github.com/boostorg/math/blob/develop/test/test_nc_f.cpp. A similar level of sanity checking would probably suffice for this function I would guess?

[JacobHass8]

Yup, tests needed.

Non central F is treated as a special case of the non-central beta (which is where most of the tests are). Non-central F tests are fairly lightweight, just there to make sure we have the transformation to non-central beta correct really: https://github.com/boostorg/math/blob/develop/test/test_nc_f.cpp. A similar level of sanity checking would probably suffice for this function I would guess?

I've added a couple of tests and documentation. The tests and documentation copy what is done for the non_central_chi_squared distribution. Is there anything else I need to do before this can be merged?

[JacobHass8]

@jzmaddock could I get a review on this when you get the chance? Are there any test cases that you can think of that I should add?

[JacobHass8]

@mborland (#1305) if you're interested, here's my first attempt at the inverse of the non-central F distribution. It was pretty much copied from the scipy implementation.