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Stein's method for geometric approximation

Part of: Combinatorial probability Markov processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Erol A. Peköz
Erol A. Peköz*
Affiliation:
University of California, Los Angeles
*
∗Postal address: Department of Mathematics, University of California, Los Angeles, CA 90024, USA.
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Abstract

The Stein–Chen method for Poisson approximation is adapted to the setting of the geometric distribution. This yields a convenient method for assessing the accuracy of the geometric approximation to the distribution of the number of failures preceding the first success in dependent trials. The results are applied to approximating waiting time distributions for patterns in coin tossing, and to approximating the distribution of the time when a stationary Markov chain first visits a rare set of states. The error bounds obtained are sharper than those obtainable using related Poisson approximations.

Keywords

STEIN'S METHODGEOMETRIC APPROXIMATIONPOISSON APPROXIMATIONHITTING TIMESPATTERNS IN COIN TOSSING

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60C05: Combinatorial probability 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 707 - 713
Copyright
Copyright © Applied Probability Trust 1996 

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