Bounds on tail probabilities of discrete distributions (Q2711572)

The aim of this paper is to examine several approaches devoted to derive lower and upper bounds for tail probabilities of discrete distributions. Section 2 of the paper presents an elementary approach in order to obtain such bounds for the following families of discrete distributions: Poisson, binomial, negative binomial, log-series, zeta, and generalized Poisson distributions. The computed bounds reveal characteristics of the specific distributional tail, and improve (sometimes) known or cumbersome results.NEWLINENEWLINENEWLINESection 3 provides refinements of the bounds in Section 2, while Section 4 extends the method of importance sampling identity to the log-series and the negative binomial distributions. The final Section 5 gives a detailed comparison of the various bounds for the Poisson, log-series, and the negative binomial distributions, illustrating the quality of the computed bounds.