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Non‐parametric estimation for semi‐Markov kernels with application to reliability analysis

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  • B. Ouhbi
  • N. Limnios

Abstract

The authors consider an irreducible Markov renewal process (MRP) with a finite number of states. Their aim is to derive estimators of a censored MRP with a finite number of states either in a fixed time T or in the Nth jump. The estimators given here are seen to be of the Kaplan‐Meier type. The asymptotic properties these estimators are given. The reliability of a semi‐Markov system model is examined numerically by the estimators, and a comparison is made with estimators obtained by Lagakos et al. © 1996 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmda:v:12:y:1996:i:4:p:209-220
    DOI: 10.1002/(SICI)1099-0747(199612)12:43.0.CO;2-T
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    Cited by:

    1. 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.
    2. Salim Bouzebda & Chrysanthi Papamichail & Nikolaos Limnios, 2018. "On a multidimensional general bootstrap for empirical estimator of continuous-time semi-Markov kernels with applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 49-86, January.
    3. 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.

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