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Minimum and maximum distances between failures in binary sequences

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  • Makri, Frosso S.

Abstract

The minimum and maximum distances denoting the extreme numbers of successes between two successive failures in binary sequences, are considered. Exact marginal and joint probability distributions of these statistics are obtained via combinatorial analysis. Applications related to urn models and system reliability are studied and clarify further the theoretical results.

Suggested Citation

  • Makri, Frosso S., 2011. "Minimum and maximum distances between failures in binary sequences," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 402-410, March.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:3:p:402-410
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    References listed on IDEAS

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    1. M. Koutras, 1996. "On a waiting time distribution in a sequence of Bernoulli trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 789-806, December.
    2. Eryilmaz, Serkan & Kan, Cihangir & Akici, Fatih, 2009. "Consecutive k-within-m-out-of-n:F system with exchangeable components," MPRA Paper 26838, University Library of Munich, Germany.
    3. Anish Sarkar & Kanwar Sen & Anuradha, 2004. "Waiting time distributions of runs in higher order Markov chains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 317-349, June.
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    1. 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.
    2. Frosso Makri & Zaharias Psillakis, 2013. "Exact distributions of constrained (k, ℓ) strings of failures between subsequent successes," Statistical Papers, Springer, vol. 54(3), pages 783-806, August.

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