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Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  30 January 2018

M. Bondareva
M. Bondareva*
Affiliation:
University of Rochester
*
∗ Postal address: William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627, USA. Email address: mariya.bondareva@simon.rochester.edu
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Abstract

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In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

Keywords

Central limit theoremPoisson distributionmonotonic approximation

MSC classification

Primary: 60E05: Distributions
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 4 , December 2013 , pp. 909 - 917
Copyright
© Applied Probability Trust 

References

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