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Generalizations of distributions related to ( $$k_1,k_2$$ k 1 , k 2 )-runs

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  • A. N. Kumar

    (Indian Institute of Technology Madras)

  • N. S. Upadhye

    (Indian Institute of Technology Madras)

Abstract

The paper deals with three generalized dependent setups arising from a sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these setups and their waiting time. Also, explicit forms of probability generating function and probability mass function are obtained. Finally, two applications to demonstrate the relevance of the results are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:2:d:10.1007_s00184-018-0668-x
    DOI: 10.1007/s00184-018-0668-x
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    References listed on IDEAS

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    1. 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.
    2. N. Balakrishnan & S. Mohanty & S. Aki, 1997. "Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 155-169, March.
    3. 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.
    4. 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.
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    Cited by:

    1. Kumar, Amit N. & Kumar, Poleen, 2024. "A negative binomial approximation to the distribution of the sum of maxima of indicator random variables," Statistics & Probability Letters, Elsevier, vol. 208(C).
    2. Xian Zhao & Yanbo Song & Xiaoyue Wang & Zhiyue Lv, 2022. "Distributions of $$({k}_{1},{k}_{2},\dots ,{k}_{m})$$ ( k 1 , k 2 , ⋯ , k m ) -runs with Multi-state Trials," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2689-2702, December.

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