Name
Abstract | ||
|---|---|---|
Let X, B, and Y be the Dirichlet, Bernoulli, and beta-independent random variables such that, X similar to 2)(a(0), ..., a(d)), Pr(B = (0,..., 0, 1, 0,..., 0)) = a(j)/a with a = Sigma(d)(1=0) ai and Y similar to beta (1, a). Then, as proved by Sethuraman (1994), X similar to 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 above result holds when B follows Bk (a(0),.., a(d)) and when Y similar to beta(k, a). We extend it even more generally to the case where X and B are random probabilities such that X is Dirichlet and B is quasiBernoulli. Finally, the case where the integer k is replaced by a positive number c is considered when a(0) =... = a(d) = 1. |
Year | Venue | Keywords |
|---|---|---|
2014 | JOURNAL OF APPLIED PROBABILITY | Perpetuities, Dirichlet process, Ewens' distribution, quasi-Bernoulli law, probabilities on a tetrahedron, T-c transform, stationary distribution |
Field | DocType | Volume |
Bernoulli distribution,Integer,Random variable,Combinatorics,Dirichlet process,Generalized Dirichlet distribution,Stationary distribution,Dirichlet distribution,Mathematics,Bernoulli's principle | Journal | 51 |
Issue | ISSN | Citations |
2 | 0021-9002 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pawel Hitczenko | 1 | 52 | 15.48 |
| Gérard Letac | 2 | 4 | 2.50 |