Advances in Applied Probability

Stein's method and stochastic orderings

Fraser Daly, Claude Lefèvre, and Sergey Utev

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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 approximations of a sum of dependent Bernoulli random variables, for example, k-runs in independent and identically distributed Bernoulli trials. Other applications include approximation by polynomial birth-death distributions.

Article information

Source
Adv. in Appl. Probab., Volume 44, Number 2 (2012), 343-372.

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1339878715

Digital Object Identifier
doi:10.1239/aap/1339878715

Mathematical Reviews number (MathSciNet)
MR2977399

Zentralblatt MATH identifier
1276.62015

Subjects
Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Stein's method birth-death process stochastic ordering total variation distance (in)dependent indicators (translated) Poisson approximation total negative and positive dependence (approximate) local dependence polynomial birth-death approximation k-runs

Citation

Daly, Fraser; Lefèvre, Claude; Utev, Sergey. Stein's method and stochastic orderings. Adv. in Appl. Probab. 44 (2012), no. 2, 343--372. doi:10.1239/aap/1339878715. https://projecteuclid.org/euclid.aap/1339878715


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