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.
Citation
M. Bondareva. "Nondecreasing lower bound on the Poisson cumulative distribution function for z standard deviations above the mean." J. Appl. Probab. 50 (4) 909 - 917, December 2013. https://doi.org/10.1239/jap/1389370089
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