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Limit laws in the best of 2n ‐ 1 bernoulli trials

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  • Richard A. Groeneveld
  • Barry C. Arnold

Abstract

A series of independent Bernoulli trials is considered in which either an outcome of type A or type B occurs at each trial. The series terminates when n outcomes of one type have occurred. Two observable random variables of interest are the total number of outcomes in the series and the number of outcomes of the “losing kind.” Two methods of approximation of the expectations of these random variables for large n are obtained and compared. The limiting distribution of the number of outcomes of the “losing kind” is considered when a beta distribution is assigned to p.

Suggested Citation

  • Richard A. Groeneveld & Barry C. Arnold, 1984. "Limit laws in the best of 2n ‐ 1 bernoulli trials," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 275-281, June.
    • Handle: RePEc:wly:navlog:v:31:y:1984:i:2:p:275-281
    DOI: 10.1002/nav.3800310209
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    Cited by:

    1. H. N. Nagariaja & W. T. Chan, 1989. "On the number of games played in a best of (2n – 1) series," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 297-310, June.

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