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Beta-binomial distribution : ウィキペディア英語版 | Beta-binomial distribution \!| | kurtosis = See text| | entropy =| | mgf = | | char = | }} In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the probability of success at each trial is not fixed but random and follows the beta distribution. It is frequently used in Bayesian statistics, empirical Bayes methods and classical statistics as an overdispersed binomial distribution. It reduces to the Bernoulli distribution as a special case when ''n'' = 1. For ''α'' = ''β'' = 1, it is the discrete uniform distribution from 0 to ''n''. It also approximates the binomial distribution arbitrarily well for large ''α'' and ''β''. The beta-binomial is a one-dimensional version of the Dirichlet-multinomial distribution, as the binomial and beta distributions are special cases of the multinomial and Dirichlet distributions, respectively. ==Motivation and derivation==
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