haskell / haskell/statistics

Problems with Student-T distribution

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Bug
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Haskell
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Description

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
```haskell
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!

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