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A Compound Poisson Approximation Inequality

Part of: Markov processes Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Erol A. Peköz
Erol A. Peköz*
Affiliation:
Boston University
*
∗ Postal address: School of Management, Boston University, 595 Commonwealth Avenue, Boston, MA 02215, USA. Email address: pekoz@bu.edu
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Abstract

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We give conditions under which the number of events which occur in a sequence of m-dependent events is stochastically smaller than a suitably defined compound Poisson random variable. The results are applied to counts of sequence pattern appearances and to system reliability. We also provide a numerical example.

Keywords

Compound Poisson approximationstochastic inequalitypatterns in coin tossingdependent events

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62E17: Approximations to distributions (nonasymptotic) 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Short Communications
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 282 - 288
Copyright
© Applied Probability Trust 2006 

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