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Waiting Time Distributions Associated with Runs of Fixed Length in Two-State Markov Chains

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  • M. Koutras

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  • M. Koutras, 1997. "Waiting Time Distributions Associated with Runs of Fixed Length in Two-State Markov Chains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 123-139, March.
    • Handle: RePEc:spr:aistmt:v:49:y:1997:i:1:p:123-139
    DOI: 10.1023/A:1003118807148
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    Citations

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    Cited by:

    1. Markos V. Koutras & Sotirios Bersimis & Demetrios L. Antzoulakos, 2006. "Improving the Performance of the Chi-square Control Chart via Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 409-426, September.
    2. Kiyoshi Inoue & Sigeo Aki, 2011. "Bivariate Fibonacci polynomials of order k with statistical applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 197-210, February.
    3. Masayuki Uchida, 1998. "Joint Distributions of Numbers of Success-runs Until the First Consecutive k Successes in a Higher-Order Two-State Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 203-222, June.
    4. S. Chadjiconstantinidis & M. V. Koutras & F. S. Milienos, 2023. "The distribution of extended discrete random sums and its application to waiting time distributions," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
    5. Yong Kong, 2019. "Decoupling Combinatorial Complexity: a Two-Step Approach to Distributions of Runs," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 789-803, September.
    6. M. Koutras & S. Bersimis & D. Antzoulakos, 2008. "Bivariate Markov chain embeddable variables of polynomial type," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 173-191, March.
    7. 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;The Institute of Statistical Mathematics, vol. 55(4), pages 865-884, December.
    8. Stathis Chadjiconstantinidis & Markos V. Koutras, 1999. "Measures of component importance for markov chain imbeddable reliability structures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 613-639, September.
    9. A. N. Kumar & N. S. Upadhye, 2019. "Generalizations of distributions related to ( $$k_1,k_2$$ k 1 , k 2 )-runs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 249-268, March.
    10. Markos V. Koutras & Serkan Eryilmaz, 2017. "Compound Geometric Distribution of Order k," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 377-393, June.
    11. Qing Han & Sigeo Aki, 2000. "Waiting Time Problems in a Two-State Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 778-789, December.
    12. Xiaoyan Zhu & Mahmoud Boushaba & Abdelmoumene Boulahia & Xian Zhao, 2019. "A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components," Journal of Risk and Reliability, , vol. 233(3), pages 328-337, June.
    13. James C. Fu & W. Y. Wendy Lou, 2007. "On the Normal Approximation for the Distribution of the Number of Simple or Compound Patterns in a Random Sequence of Multi-state Trials," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 195-205, June.
    14. Kiyoshi Inoue, 2004. "Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 143-168, March.
    15. 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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