Stochastic Ordering Among Success Runs Statistics in a Sequence of Exchangeable Binary Trials
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A new scheme-distribution-based representation is presented for the cumulative distribution function of the number of success runs of length k in a sequence of exchangeable binary trials. By utilizing this new representation, some stochastic ordering results are obtained to compare success runs. The results are illustrated for beta-binomial distributions of order k.
KeywordsBinomial distribution of order k Exchangeable binary random variables Stochastic ordering Success runs
Mathematics Subject Classification (2010)60E05 62E15
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The author thanks the referees for their helpful comments and suggestions, which were very useful in improving this article.
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