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Number of appearances of events in random sequences: a new generating function approach to Type II and Type III runs

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  • Yong Kong

    (Yale University)

Abstract

Distributions of runs of length at least k (Type II runs) and overlapping runs of length k (Type III runs) are derived in a unified way using a new generating function approach. A new and more compact formula is obtained for the probability mass function of the Type III runs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:2:d:10.1007_s10463-015-0549-2
    DOI: 10.1007/s10463-015-0549-2
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    References listed on IDEAS

    as
    1. Yong Kong, 2015. "Distributions of Runs Revisited," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(22), pages 4663-4678, November.
    2. Kong, Yong, 2006. "Distribution of Runs and Longest Runs: A New Generating Function Approach," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1253-1263, September.
    3. M. Koutras & V. Alexandrou, 1995. "Runs, scans and URN model distributions: A unified Markov chain approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 743-766, December.
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