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Distributions of Runs Revisited

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  • Yong Kong

Abstract

Distributions of runs have important applications in many fields, including biological sequence analysis. The generating function (GF) method provides a unified approach to tackle different run-related problems in multistate trials. By utilizing this method, various run-related distributions are derived in a systematic way for both conditional and unconditional models. The GF approach also naturally yields the asymptotic distributions. For all the distributions considered, the limiting distributions are Gaussian, with mean, variance, and covariance linear functions in the size of the system.

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  • Yong Kong, 2015. "Distributions of Runs Revisited," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(22), pages 4663-4678, November.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:22:p:4663-4678
    DOI: 10.1080/03610926.2013.793350
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    Cited by:

    1. Yong Kong, 2019. "Decoupling Combinatorial Complexity: a Two-Step Approach to Distributions of Runs," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 789-803, September.
    2. Yong Kong, 2017. "Number of appearances of events in random sequences: a new generating function approach to Type II and Type III runs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 489-495, April.

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