The Annals of Applied Probability

Stein's Method for Compound Poisson Approximation: The Local Approach

Malgorzata Roos

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Abstract

In the present paper, compound Poisson approximation by Stein's method is considered. A general theorem analogous to the local approach for Poisson approximation is proved. It is then applied to a reliability problem involving the number of isolated vertices in the rectangular lattice on the torus.

Article information

Source
Ann. Appl. Probab., Volume 4, Number 4 (1994), 1177-1187.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004910

Digital Object Identifier
doi:10.1214/aoap/1177004910

Mathematical Reviews number (MathSciNet)
MR1304780

Zentralblatt MATH identifier
0816.60021

JSTOR
links.jstor.org

Subjects
Primary: 05C90: Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]
Secondary: 60C05: Combinatorial probability 60F05: Central limit and other weak theorems 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

Keywords
Stein-Chen method compound Poisson distribution rate of convergence reliability theory isolated vertices $k$-out-of-$n$ rectangular lattice

Citation

Roos, Malgorzata. Stein's Method for Compound Poisson Approximation: The Local Approach. Ann. Appl. Probab. 4 (1994), no. 4, 1177--1187. doi:10.1214/aoap/1177004910. https://projecteuclid.org/euclid.aoap/1177004910


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