AbstractA generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m, β, θ)= θx (1 ‐ θ)m+βx—x for x=0, 1, …, and zero otherwise, where m>0, 0<θ<1 and β=0 or 1≦β<θ−1. The Bayes estimators for a number of parametric functions of θ when m and β are known are derived. The prior information on θ may be given by a beta distribution, B(a, b), to which no subjective significance is attached. It has been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayes estimate of P(X=k) to the corresponding ML estimate and the MVU estimate for any given sample to the order n−1 for different values of k..