Problems with Student-T distribution

[Shimuuar]

So far following problems with Student-T distribution were identified:

1. quantile lose precision for p≈0.5 since x becomes close to 1, while p is near zero

quantile :: StudentT -> Double -> Double
quantile (StudentT ndf) p
  | p >= 0 && p <= 1 =
    let x = invIncompleteBeta (0.5 * ndf) 0.5 (2 * min p (1 - p))
    in case sqrt $ ndf * (1 - x) / x of
         r | p < 0.5   -> -r
           | otherwise -> r

2. Both precision and performance suffer greatly for large degrees of freedom. Reason is likely incomplete beta and its inverse perform poorly for large parameters. However distribution becomes close to normal so other approximations could work!

[Shimuuar]

RE 2.

Quick experimentation with mpmath shows that precision becomes worse for larger NDF. (N of ulps of error proportional to NDF). For very large N mpmath fails itself which I think doesn't bring any good news for algorithm being used...