hypergeometric6

]> hypergeometric6

\begin{array}{rcl} mean & = & \frac{r n}{N} \\ mode & = & floor (\frac{(r + 1) (n + 1)}{N + 2}) \\ variance & = & \frac{r (\frac{n}{N}) (1 - \frac{n}{N}) (N - r)}{(N - 1)} \\ skewness & = & \frac{(N - 2 n) \sqrt{(N - 1)} (N - 2 r)}{\sqrt{r n (N - n) (N - r)} (N - 2)} \\ kurtosis excess & = & (\frac{N^{2} (N - 1)}{r (N - 2) (N - 3) (N - r)}) (\frac{N (N + 1) - 6 N (N - r)}{n (N - n)} + \frac{3 r (N - r) (N + 6)}{N^{2}} - 6) \end{array}