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Specific formulae for some success run distributions

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  • Godbole, Anant P.

Abstract

Let N(k)n denote the number of success runs of length k ([greater-or-equal, slanted] 1) in n Bernoulli trials. A specific formula is derived for P(N(k)n = x) which is alternative to the one established by Philippou and Makri (1986) and Hirano (1986) and which is in a form suitable for the computation of asymptotic distributions (as in Godbole, 1990a, b); recall that N(k)n is said to have a binomial distribution of order k. In a similar fashion, different formulae are obtained for the geometric, negative binomial and Poisson distributions of order k (introduced by Philippou, Georghiou and Philippou, 1983.

Suggested Citation

  • Godbole, Anant P., 1990. "Specific formulae for some success run distributions," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 119-124, July.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:2:p:119-124
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    Citations

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    Cited by:

    1. Wendy Lou, W. Y., 1997. "An application of the method of finite Markov chain imbedding to runs tests," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 155-161, January.
    2. Muselli, Marco, 1996. "Simple expressions for success run distributions in bernoulli trials," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 121-128, December.
    3. Koutras, M. V. & Alexandrou, V. A., 1997. "Non-parametric randomness tests based on success runs of fixed length," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 393-404, April.
    4. Christian Weiß, 2013. "Monitoring kth order runs in binary processes," Computational Statistics, Springer, vol. 28(2), pages 541-562, April.
    5. Frosso Makri & Andreas Philippou, 2005. "On binomial and circular binomial distributions of orderk forl-overlapping success runs of lengthk," Statistical Papers, Springer, vol. 46(3), pages 411-432, July.
    6. Demetrios Antzoulakos & Stathis Chadjiconstantinidis, 2001. "Distributions of Numbers of Success Runs of Fixed Length in Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 599-619, September.

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