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SOME NEW BOUNDS AND APPROXIMATIONS ON TAIL PROBABILITIES OF THE POISSON AND OTHER DISCRETE DISTRIBUTIONS

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  11 October 2018

Steven G. From  and
Andrew W. Swift
Steven G. From
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA E-mail: [email protected]; [email protected]
Andrew W. Swift
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA E-mail: [email protected]; [email protected]
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Abstract

In this paper, we discuss new bounds and approximations for tail probabilities of certain discrete distributions. Several different methods are used to obtain bounds and/or approximations. Excellent upper and lower bounds are obtained for the Poisson distribution. Excellent approximations (and not bounds necessarily) are also obtained for other discrete distributions. Numerical comparisons made to previously proposed methods demonstrate that the new bounds and/or approximations compare very favorably. Some conjectures are made.

Keywords

approximations and boundsdiscrete distributionsPoisson distributiontail probabilities

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62E15: Exact distribution theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 1 , January 2020 , pp. 53 - 71
Copyright
Copyright © Cambridge University Press 2018 

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