ChiSquared can return NaN values when requesting the inverse CDF

[IceTDrinker]

Hello,

First of all thanks a lot for the work on statrs, it is very nice to have such a library in rust !

I know computing some of the statistics are hard computational problems (as in dealing with floating point precision and writing the proper algorithms matching theoretical maths formulas).

I would like to report the following case which fails :

use statrs::distribution::{ChiSquared, ContinuousCDF};

pub fn main() {
    let alpha = 0.01;

    let df = 129757f64;
    let chi2 = ChiSquared::new(df).unwrap();
    let chi2_lower = chi2.inverse_cdf(alpha / 2.0);
    let chi2_upper = chi2.inverse_cdf(1.0 - alpha / 2.0);
    if !(chi2_lower.is_finite() && chi2_upper.is_finite()) {
        dbg!(chi2_lower);
        dbg!(chi2_upper);
        panic!("{df}");
    }
}

I am aware these values are extreme, chi2_upper produces a NaN.

I prefer reporting it because the function docstring does not indicate the possibility to encounter NaNs and other software like scipy will give a finite answer.

It's now possible to use scipy's special functions in rust using the wrapper around their xsf library :

• xsf library from scipy (c++) : https://github.com/scipy/xsf/
• wrapper : https://github.com/jorenham/xsf-rust

It may be of interest to you for testing purposes.

I still think having rust code able to compute special math functions has value (to avoid dependency on a C++ compiler or tooling), I have no idea what the best course of action for statrs is.

I know there are other combinations of parameters which will make the inverse CDF fail for the ChiSquared distribution.

Cheers