A characterization of multinomial and negative multinomial distributions
Konanur G. Janardan · Scandinavian Actuarial Journal · 1974
The intent of this paper is to show that the independent random vectors x and y have multinomial (negative mUltinomial) distributions with the same parameter vector ø, and the other parameters being respectively m and n if and only if the conditional distribution of x given x + y is multivariate hypergeometric (multivariate inverse hypergeometric) distribution with parameters m + n = N and x + y = N.