Stein's method and stochastic orderings

2009/12/08 by Fraser Daly, Daly, Fraser, Claude Lefèvre +3 · 1 citation
Mathematics · #60J80 (Secondary) #62E17 (Primary) 60F05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.0912.1448

openalex publication_date 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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