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Distribution theory of runs via exchangeable random variables

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  • Schuster, Eugene F.

Abstract

The conditional distribution theory of the number of runs R in a randomly ordered sequence of length N = m + n of two types of symbols, say m of type F (failures) and n of type S (successes), is studied via the representation R = 1 + [summation operator]m + 1k = 1[alpha]kIk where I1,..., Im + 1 are exchangeable Bernoulli random variables with [alpha]1 = [alpha]m + 1 = 1 and [alpha]k = 2, otherwise. This exchangeable representation of R, and related statistics, considerably facilitates the study of distribution theory of these statistics.

Suggested Citation

  • Schuster, Eugene F., 1991. "Distribution theory of runs via exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 379-386, May.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:5:p:379-386
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    Cited by:

    1. Frosso S. Makri & Zaharias M. Psillakis, 2011. "On Success Runs of Length Exceeded a Threshold," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 269-305, June.

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