C. G. E. Boender, A. H. G. Rinnooy Kan, A Bayesian Analysis of the Number of Cells of a Multinomial Distribution, Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 32, No. 1/2, Proceedings of the 1982 I.O.S. Annual Conference on Practical Bayesian Statistics (Mar. - Jun., 1983), pp. 240-248
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Boender et al. (1983) studied this question.
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