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Distributions of patterns of two successes separated by a string of k-2 failures

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  • Spiros Dafnis
  • Andreas Philippou

    ()

  • Demetrios Antzoulakos
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    File URL: http://hdl.handle.net/10.1007/s00362-010-0340-7
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    Bibliographic Info

    Article provided by Springer in its journal Statistical Papers.

    Volume (Year): 53 (2012)
    Issue (Month): 2 (May)
    Pages: 323-344

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    Handle: RePEc:spr:stpapr:v:53:y:2012:i:2:p:323-344

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    Web page: http://www.springer.com/statistics/business/journal/362

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    Related research

    Keywords: Success runs; Patterns; Distributions of order k ; Waiting time distributions; Markov chains; Recurrence relations; Probability generating function; Probability mass function; Moments; Reliability;

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    1. M. Koutras & V. Alexandrou, 1995. "Runs, scans and URN model distributions: A unified Markov chain approach," Annals of the Institute of Statistical Mathematics, Springer, vol. 47(4), pages 743-766, December.
    2. 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.
    3. Qing Han & Sigeo Aki, 1999. "Joint Distributions of Runs in a Sequence of Multi-State Trials," Annals of the Institute of Statistical Mathematics, Springer, vol. 51(3), pages 419-447, September.
    4. Philippou, Andreas N. & Makri, Frosso S., 1986. "Successes, runs and longest runs," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 211-215, June.
    5. D. Antzoulakos & S. Bersimis & M. Koutras, 2003. "On the distribution of the total number of run lengths," Annals of the Institute of Statistical Mathematics, Springer, vol. 55(4), pages 865-884, December.
    6. Philippou, Andreas N. & Makri, Frosso S., 1986. "Successes, runs and longest runs," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 101-105, March.
    7. Philippou, Andreas N. & Georghiou, Costas & Philippou, George N., 1983. "A generalized geometric distribution and some of its properties," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 171-175, June.
    8. Kiyoshi Inoue & Sigeo Aki, 2003. "Generalized binomial and negative binomial distributions of orderk by thel-overlapping enumeration scheme," Annals of the Institute of Statistical Mathematics, Springer, vol. 55(1), pages 153-167, March.
    9. Ling, K. D., 1989. "A new class of negative binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 371-376, April.
    10. Anish Sarkar & Kanwar Sen & Anuradha, 2004. "Waiting time distributions of runs in higher order Markov chains," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(2), pages 317-349, June.
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