diff --git a/docs/distributions.md b/docs/distributions.md index 8abea06..47f2fea 100644 --- a/docs/distributions.md +++ b/docs/distributions.md @@ -590,24 +590,6 @@ distributions. The proofs are not published, but it isn't difficult to validate their correctness, e.g. numerically, or symbolically with sympy or wolfram alpha / mathematica. -### Bernoulli - -Surprisingly, the L-moments of the discrete -[Bernoulli distribution](https://wikipedia.org/wiki/Bernoulli_distribution) -[@uspensky1937], can't be expressed as easily as the distribution itself: - -\[ -\tlmoment{s, t}{r} = - \frac{(-1)^r}{r} - (1 - p)^{s + 1} - \jacobi{r + t - 1}{s + 1}{-t - 1}{2p - 1} - + \ffact{1}{r} -\] - -Here, \( \jacobi{n}{\alpha}{\beta}{x} \) is a -[Jacobi polynomial](#def-jacobi) (although it's not orthogonal for -\( t >= 0 \), since \( \beta > -1 \) does not hold). - ### PFD With support on the interval \( (0, 1] \) and shape parameter