Nondecreasing lower bound on the poisson cumulative distribution

• Autores: M. BONDAREVA
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 4, 2013, págs. 909-917
• Idioma: inglés
• DOI: 10.1017/s0021900200013693
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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