Negative multinomial distribution
= Negative multinomial distribution
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Counts of several categories before a fixed number of stopping-category outcomes have a negative multinomial distribution. For one stopping outcome of probability $r=1-\alpha-\beta$, the two-count mass function is $r\binom{x+y}{x}\alpha^x\beta^y$. Its <probability generating function> is $r/(1-\alpha s-\beta t)$ and its means are $\alpha/r$ and $\beta/r$.