Abstract
The gamma-Poisson and beta-binomial mixture distributions are used for analyzing count-valued data, and the estimation of the hyper-parameters including the shape and/or scale parameters is important in the empirical Bayes inference. The maximum likelihood method requires the nested loops for solving the non-linear equations at each step of iteration in the EM algorithm. To avoid the extra loops, we derive the closed-form updating procedures at each step of iteration by using the score-adjusted method. The performance is compared by simulation with the maximum likelihood estimators.
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