Abstract
A useful recurrence relation for calculating the probabilities of the multivariare negative binomial distrtibution of order k is obtained. Analogous recurrences are also established for the type I, type II and extended multivariate negative binomial distributions of the same order. The present paper extends to the multivariate case the work of Philippou and Antzoulakos (1989) on calculating the probabilities of the multi-parameter negative binomial distribution of order k.
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