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.
ASJC Scopus subject areas
- Applied Mathematics