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Dirichlet and Quasi-Bernoulli Laws for Perpetuities

2014
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Journal of Applied Probability
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Let X, B, and Y be the Dirichlet, Bernoulli, and beta-independent random variables such that X ~ D (a 0, ..., a d ), Pr(B = (0, ..., 0, 1, 0, ..., 0)) = a i / a with a = ∑ i=0 d a i , and Y ~ β(1, a). Then, as proved by Sethuraman (1994), X ~ X(1 - Y) + BY. This gives the stationary distribution of a simple Markov chain on a tetrahedron. In this paper we introduce a new distribution on the tetrahedron called a quasi-Bernoulli distribution B k (a 0, ..., a d ) with k an integer such that the

doi:10.1239/jap/1402578633
fatcat:mvk2dsbhsra4to4ua5zzczlode