Altham (1978) introduced the discrete distribution f(x; ????, ????) = c(????, ????)

( n x

)

????x

(1 − ????)

n−x

????x(n−x)

, x = 0, 1,…, n, where c(????, ????) is a normalizing constant. Show that this is in the two-parameter exponential family and that the binomial occurs when ???? = 1. (Altham noted that overdispersion occurs when ???? < 1. Lindsey and Altham (1998) used this as the basis of an alternative model to the beta-binomial.)