Beta-Binomially and Dirichlet-multinomially Distributed Random Number Generation Based on the Polya Urn Scheme

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  • Beta Binomially and Dirichlet multinomi

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A statistical model for describing mixing states of a binary mixture was proposed by Yoshizawa and Shindo [1]. This model, based on a beta-binomial distribution, enables one to describe various variations of characteristics in space and time scales. In this paper, an algorithm for generating beta-binomially distributed random numbers is presented on the basis of the Polya urn scheme. Focusing on the ratio changes enables one to successfully eliminate an overflow problem which occurs in the scheme. Although the algorithm is not perfectly efficient, it is precise and easily understandable. An algorithm for the n-ary case, Dirichlet-multinomially distributed random number generation, is also presented as a natural extension of the binary case.

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