On Dirichlet Multinomial Distributions
نویسندگان
چکیده
Dedicated to Professor Y. S. Chow on the Occasion of his 80th Birthday By Robert W. Keener and Wei Biao Wu Abstract Let Y have a symmetric Dirichlet multinomial distributions in R, and let Sm = h(Y1)+· · ·+h(Ym). We derive a central limit theorem for Sm as the sample size n and the number of cells m tend to infinity at the same rate. The rate of convergence is shown to be of order m. The approach is based on approximation of marginal distributions for the Dirichlet multinomial distribution by negative binomial distributions, and a blocking technique similar to that used to study renormalization groups in statistical physics. These theorems generalize and refine results for the classical occupancy problem.
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