Stein's method and stochastic orderings

Details Stein's method and stochastic orderings Stein's method and stochastic orderings

2009-12-08

arxiv.org/abs/0912.1448v1

Mathematics

Probability

39 pages, 1 table. Submitted to Advances in Applied Probability

Scientific paper

A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex orders are discussed. Attention is focused on Poisson and translated Poisson approximation of a sum of dependent Bernoulli random variables, for example k-runs in i.i.d. Bernoulli trials. Other applications include approximation by polynomial birth--death distributions.

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