Negative Hypergeometric Distribution

Consider a box containing $M$ balls: $n$ red and $M-n$ blue. We randomly sample balls from the box, one at a time and without replacement, until we have picked $r$ blue balls. nhypergeom is the distribution of the number of red balls $k$ we have picked.

for $k\in 0,1,2,...,n$, where the binomial coefficients are defined as,

The cumulative distribution, survivor function, hazard function, cumulative hazard function, inverse distribution function, moment generating function, and characteristic function on the support of $k$ are mathematically intractable.

Implementation: scipy.stats.nhypergeom