Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T11:55:45.343Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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