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Some limiting distributions associated with sequences of multinomial trials

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  • B. C. Arnold
  • J. E. Angus

Abstract

A series of independent trials is considered in which one of k ≥ 2 mutually exclusive and exhaustive outcomes occurs at each trial. The series terminates when m outcomes of any one type have occurred. The limiting distribution (as m → ∞) of the number of trials performed until termination is found with particular attention to the situation where a Dirichlet distribution is assigned to the k vector of probabilities for each outcome. Applications to series of races involving k runners and to spares problems in reliability modeling are discussed. The problem of selecting a stopping rule so that the probability of the series terminating on outcome i is k−1 (i.e., a “fair” competition) is also studied. Two generalizations of the original asymptotic problem are addressed.

Suggested Citation

  • B. C. Arnold & J. E. Angus, 1983. "Some limiting distributions associated with sequences of multinomial trials," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(1), pages 1-11, March.
    • Handle: RePEc:wly:navlog:v:30:y:1983:i:1:p:1-11
    DOI: 10.1002/nav.3800300102
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