Some limiting distributions associated with sequences of multinomial trials

B. C. Arnold and J. E. Angus

Naval Research Logistics Quarterly, 1983, vol. 30, issue 1, 1-11

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.

Date: 1983
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https://doi.org/10.1002/nav.3800300102

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:30:y:1983:i:1:p:1-11

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