### 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 language | English (US) |
---|---|

Pages (from-to) | 621-640 |

Number of pages | 20 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 45 |

Issue number | 4 |

State | Published - Aug 1985 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*45*(4), 621-640.

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

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 45, no. 4, pp. 621-640.

}

TY - JOUR

T1 - PROBABILITY BOUNDS ON THE SUM OF INDEPENDENT NONIDENTICALLY DISTRIBUTED BINOMIAL RANDOM VARIABLES.

AU - Percus, Ora E.

AU - Percus, Jerome

PY - 1985/8

Y1 - 1985/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022108071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022108071&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022108071

VL - 45

SP - 621

EP - 640

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 4

ER -