User:BeyondNormality/Altham-multiplicative binomial distribution

The probability mass function of the Altham-multiplicative binomial distribution is



\mathrm{AlthamMultBin}(x; a,n,p) \equiv \Pr(X = x) = \frac{ \binom{n}{x} p^x (1-p)^{n-x} a^{x (n-x)}}{F(n)} $$


 * $$ x = 0, 1, \dots, n $$
 * $$ a \ge 0 $$
 * $$ n \in \mathbb{N}_0 $$
 * $$ 0 \le p \le 1 $$
 * $$ q = 1-p $$
 * $$ F(n) = \sum _{j=0}^n \binom{n}{j} p^j (1-p)^{n-j} a^{j (n-j)}  $$