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Joint Distributions of Numbers of Success-Runs and Failures Until the First Consecutive k Successes in a Binary Sequence

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Abstract

Joint distributions of the numbers of failures, successes andsuccess-runs of length less than k until the first consecutive k successesin a binary sequence were derived recently by Aki and Hirano (1995, Ann.Inst. Statist. Math., 47, 225-235). In this paper, we present an alternatederivation of these results and also use this approach to establish someadditional results. Extensions of these results to binary sequences of orderh are also presented.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1

    N. Balakrishnan

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  1. N. Balakrishnan
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Balakrishnan, N. Joint Distributions of Numbers of Success-Runs and Failures Until the First Consecutive k Successes in a Binary Sequence. Annals of the Institute of Statistical Mathematics 49, 519–529 (1997). https://doi.org/10.1023/A:1003170829230

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