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Bayesian approach for the reliability parameter of power Lindley distribution

Author

Listed:
  • Iman Makhdoom

    (Payame Noor University (PNU))

  • Parviz Nasiri

    (Payame Noor University (PNU))

  • Abbas Pak

    (Shahrekord University)

Abstract

This study investigates Bayesian inference on the reliability parameter $$R=P(X>Y)$$ R = P ( X > Y ) from the power Lindley (PL) distribution where X and Y are independent power Lindley random variables. Gamma distribution is used as the priors of parameters. Bayes and empirical Bayes (EB) approaches are provided in details. Based on an EB approach, hyperparameters in the prior distributions, are estimated using the method of moments and maximum likelihood estimates (MLEs). Further, noninformative and less informative priors are opted as the Bayes approaches. To estimate the reliability parameter, the posterior mode (PM) and posterior mean methods are obtained. Markov Chain Monte Carlo (MCMC) method is performed for the implementation of the posterior mean method. The accuracy of the estimation methods involving the MLEs in frequency school and the Bayesian estimate methods are investigated through the Monte Carlo simulations. An application example on a real data is performed for illustrative purpose. Finally, we will bring this research to the end with discussion on the results.

Suggested Citation

  • Iman Makhdoom & Parviz Nasiri & Abbas Pak, 2016. "Bayesian approach for the reliability parameter of power Lindley distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 7(3), pages 341-355, September.
    • Handle: RePEc:spr:ijsaem:v:7:y:2016:i:3:d:10.1007_s13198-016-0476-5
    DOI: 10.1007/s13198-016-0476-5
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    3. Singh, Bhupendra & Gupta, Puneet Kumar, 2012. "Load-sharing system model and its application to the real data set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1615-1629.
    4. Krishna, Hare & Kumar, Kapil, 2011. "Reliability estimation in Lindley distribution with progressively type II right censored sample," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 281-294.
    5. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    6. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
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