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Semi-Markov Modelling for Multi-State Systems

Author

Listed:
  • Vlad Stefan Barbu

    (Université de Rouen)

  • Alex Karagrigoriou

    (University of the Aegean)

  • Andreas Makrides

    (University of Cyprus)

Abstract

In this work we focus on multi state systems that we model by means of semi-Markov processes. The sojourn times are seen to be independent not identically distributed random variables and assumed to belong to a general class of distributions that includes several popular reliability distributions like the exponential, Weibull, and Pareto. We obtain maximum likelihood estimators of the parameters of interest and investigate their asymptotic properties. Plug-in type estimators are furnished for various quantities related to the system under study.

Suggested Citation

  • Vlad Stefan Barbu & Alex Karagrigoriou & Andreas Makrides, 2017. "Semi-Markov Modelling for Multi-State Systems," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1011-1028, December.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:4:d:10.1007_s11009-016-9510-y
    DOI: 10.1007/s11009-016-9510-y
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    References listed on IDEAS

    as
    1. Brahim Ouhbi & Nikolaos Limnios, 1999. "Nonparametric Estimation for Semi-Markov Processes Based on its Hazard Rate Functions," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 151-173, May.
    2. B. Ouhbi & N. Limnios, 1996. "Non‐parametric estimation for semi‐Markov kernels with application to reliability analysis," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 12(4), pages 209-220, December.
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    Cited by:

    1. Cindy Frascolla & Guillaume Lecuelle & Pascal Schlich & Hervé Cardot, 2022. "Two sample tests for Semi-Markov processes with parametric sojourn time distributions: an application in sensory analysis," Computational Statistics, Springer, vol. 37(5), pages 2553-2580, November.
    2. Vlad Stefan Barbu & Alex Karagrigoriou & Andreas Makrides, 2021. "Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case," Mathematics, MDPI, vol. 9(16), pages 1-17, August.

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