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

Ora E. Percus, Jerome Percus

Research output: Contribution to journalArticle

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
StatePublished - Aug 1985

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Probability Bounds
Random variables
Random variable
Upper and Lower Bounds

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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PROBABILITY BOUNDS ON THE SUM OF INDEPENDENT NONIDENTICALLY DISTRIBUTED BINOMIAL RANDOM VARIABLES. / Percus, Ora E.; Percus, Jerome.

In: SIAM Journal on Applied Mathematics, Vol. 45, No. 4, 08.1985, p. 621-640.

Research output: Contribution to journalArticle

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