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- W2077400015 abstract "Statistics denoting the numbers of success runs of length exactly equal and at least equal to a fixed length, as well as the sum of the lengths of success runs of length greater than or equal to a specific length, are considered. They are defined on both linearly and circularly ordered binary sequences, derived according to the Pólya-Eggenberger urn model. A waiting time associated with the sum of lengths statistic in linear sequences is also examined. Exact marginal and joint probability distribution functions are obtained in terms of binomial coefficients by a simple unified combinatorial approach. Mean values are also derived in closed form. Computationally tractable formulae for conditional distributions, given the number of successes in the sequence, useful in nonparametric tests of randomness, are provided. The distribution of the length of the longest success run and the reliability of certain consecutive systems are deduced using specific probabilities of the studied statistics. Numerical examples are given to illustrate the theoretical results." @default.
- W2077400015 created "2016-06-24" @default.
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- W2077400015 date "2007-12-01" @default.
- W2077400015 modified "2023-09-29" @default.
- W2077400015 title "Success run statistics defined on an urn model" @default.
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- W2077400015 doi "https://doi.org/10.1239/aap/1198177236" @default.
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