PROBABILITY BOUNDS ON THE SUM OF INDEPENDENT NONIDENTICALLY DISTRIBUTED BINOMIAL RANDOM VARIABLES.

Ora E. Percus, Jerome K. Percus

Research output: Contribution to journalArticlepeer-review

Abstract

The cumulative distribution of the sum of independent binomial random variables is investigated. After writing down exact expressions for these quantities, the authors develop a sequence of increasingly tight upper and lower bounds, given various characteristics of the underlying set of probabilities. The major tool in each case is a transformation of the probability set for which the cumulative distributions act as Lyapounov function. Their most sophisticated bounds, in which the first two cumulatives are given, are computed for a number of sets of probabilities and compared with familiar results in the literature. They are uniformly superior.

Original languageEnglish (US)
Pages (from-to)621-640
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume45
Issue number4
DOIs
StatePublished - 1985

ASJC Scopus subject areas

  • Applied Mathematics

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