Resumen de Nondecreasing lower bound on the poisson cumulative distribution

M. BONDAREVA

• In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean ?, where z and ? 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 a and parameter ?, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to ?, its ath 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