A Bayesian Approach to Negative Binamial Parameter Estimation

Some procedures that are used to calculate aggregate loss distributions and claim count distributions assume the claim count distribution is a negative binomial distribution. The parameters for the negative binomial distribution are often based on data from a small number of loss periods, and the estimates may have considerable error. A Bayesian procedure for parameter estimation allows the analyst to use some judgment when deriving the parameter estimate. This paper derives the Bayesian estimation procedure of the negative binomial parameter, p, under the assumption that the prior distribution for p is a beta distribution.