Three-Parameter Generalisation of the Beta-Binomial Distribution with Applications

摘要

A three-parameter generalisation of the beta-binomial distribution (BBD) is derived and examined. The author obtains the maximum likelihood estimates of the parameters and show that the regularity conditions for asymptotic efficiency are satisfied. To exhibit the applicability of the generalised distribution it is shown how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally an empirical Bayes estimate of a binomial proportion based on the generalized beta distribution used in this study is derived.