Journal of Applied Probability

Nondecreasing lower bound on the Poisson cumulative distribution function for z standard deviations above the mean

M. Bondareva

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 50, Number 4 (2013), 909-917.

Dates
First available in Project Euclid: 10 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1389370089

Digital Object Identifier
doi:10.1239/jap/1389370089

Mathematical Reviews number (MathSciNet)
MR3161363

Zentralblatt MATH identifier
1291.60026

Subjects
Primary: 60E05: Distributions: general theory

Keywords
Central limit theorem Poisson distribution monotonic approximation

Citation

Bondareva, M. Nondecreasing lower bound on the Poisson cumulative distribution function for z standard deviations above the mean. J. Appl. Probab. 50 (2013), no. 4, 909--917. doi:10.1239/jap/1389370089. https://projecteuclid.org/euclid.jap/1389370089


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