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On success runs in a sequence of dependent trials with a change point

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  • Eryilmaz, Serkan

Abstract

Let Xii=1n be a sequence of n dependent binary trials such that the first n1 in Xii=1n are of type 1 and follow an exchangeable joint distribution denoted by L1, and the last n2 elements in Xii=1n are of type 2 and follow an exchangeable joint distribution denoted by L2, where n1+n2=n. That is, the trials within the same group are exchangeable dependent, and the trials in different groups are dependent in a general sense. The exact distributions of the number of success runs of length k in Xii=1n are obtained under nonoverlapping and at least schemes.

Suggested Citation

  • Eryilmaz, Serkan, 2018. "On success runs in a sequence of dependent trials with a change point," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 91-98.
    • Handle: RePEc:eee:stapro:v:132:y:2018:i:c:p:91-98
    DOI: 10.1016/j.spl.2017.09.007
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    References listed on IDEAS

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    1. Arapis, Anastasios N. & Makri, Frosso S. & Psillakis, Zaharias M., 2016. "On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 45-54.
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    4. Makri, Frosso S. & Psillakis, Zaharias M. & Arapis, Anastasios N., 2015. "Length of the minimum sequence containing repeats of success runs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 28-37.
    5. Philippou, Andreas N. & Makri, Frosso S., 1986. "Successes, runs and longest runs," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 101-105, March.
    6. Serkan Eryilmaz, 2017. "The concept of weak exchangeability and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 259-271, April.
    7. Philippou, Andreas N. & Makri, Frosso S., 1986. "Successes, runs and longest runs," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 211-215, June.
    8. Frosso Makri & Zaharias Psillakis, 2011. "On runs of length exceeding a threshold: normal approximation," Statistical Papers, Springer, vol. 52(3), pages 531-551, August.
    9. 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.
    10. 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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