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Stein factor bounds for random variables

Part of: Distribution theory - Probability Distribution theory Markov processes

Published online by Cambridge University Press:  14 July 2016

Graham V. Weinberg
Graham V. Weinberg*
Affiliation:
University of Melbourne
*
∗ Postal address: Teletraffic Research Centre, University of Adelaide, Adelaide 5050, Australia. Email address: gweinberg@trc.adelaide.edu.au
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Abstract

A probabilistic proof of a Stein factor bound is given, extending the Poisson case in Xia (1999).

Keywords

Distributional approximationsStein's methodbirth and death processesStein's factors

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62E17: Approximations to distributions (nonasymptotic) 60J27: Continuous-time Markov processes on discrete state spaces
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1181 - 1187
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

[1] Asmussen, S. (1987). Applied Probability and Queues. John Wiley, New York.Google Scholar
[2] Barbour, A. D. (1988). Stein's method and Poisson process convergence. J. Appl. Prob. 25A, 175–184.CrossRefGoogle Scholar
[3] Barbour, A. D., and Brown, T. C. (1992). Stein's method and point process approximation. Stoch. Proc. Appl. 43, 9–31.CrossRefGoogle Scholar
[4] Barbour, A. D., Holst, L., and Janson, S. (1992). Poisson Approximation. Oxford University Press.CrossRefGoogle Scholar
[5] Brown, T. C., and Phillips, M. J. (1999). Negative binomial approximation with Stein's method. Methodol. Comput. Appl. Prob. 1, 407–421.CrossRefGoogle Scholar
[6] Weinberg, G. V. (1999). On the role of non-uniform bounds and the probabilistic method in applications of the Stein–Chen method. PhD Thesis, University of Melbourne.Google Scholar
[7] Xia, A. (1999). A probabilistic proof of Stein's factors. J. Appl. Prob. 36, 287–290.CrossRefGoogle Scholar