STEIN'S METHOD AND STOCHASTIC ORDERINGS

被引：16

作者：

Daly, Fraser ^{[1
]}

Lefevre, Claude ^{[2
]}

Utev, Sergey ^{[3
]}

机构：

[1] Univ Zurich, CH-8006 Zurich, Switzerland

[2] Univ Libre Bruxelles, Dept Math, B-1050 Brussels, Belgium

[3] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

ADVANCES IN APPLIED PROBABILITY | 2012年 / 44卷 / 02期

关键词：

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; BINOMIAL APPROXIMATION; POISSON; VARIABLES; SUMS;

D O I：

10.1017/S0001867800005632

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：343 / 372

页数：30

共 30 条

[1]

[Anonymous], METHODOLOGY COMPUT A

[2]

[Anonymous], ESAIM PROB STAT

[3]

[Anonymous], 1986, I MATH STAT LECT NOT

[4]

[Anonymous], ANN APPL PROB