User:BeyondNormality/Anderson distribution

The probability mass function of the Anderson distribution is



\mathrm{Anderson}(x; K,N) \equiv \Pr(X = x) = \sum _{j=0}^{N-x} \frac{(-1)^j}{j! x!} \left(\frac{(-j+N-x)!}{N!}\right)^{K-2} $$


 * $$ x = 0, 1, \dots, N $$
 * $$ K \in \mathbb{N} - \{ 0,1 \}  $$
 * $$ N \in \mathbb{N}_0  $$

Probability Generating Function



\begin{align} G(t) & = \,_1F_{K-1}(-N; \underbrace{-N, \dots, -N}_{K-1}; (-1)^K (t-1)) \\ & = (N!)^{2-K} \sum _{j=0}^N \frac{(t-1)^j ((N-j)!)^{K-2}}{j!} \end{align} $$