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Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions

Author

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  • Mehdi Basikhasteh

    (Islamic Azad University)

  • Iman Makhdoom

    (Payame Noor University(PNU))

Abstract

The bivariate Weibull-Geometric (BWG) distribution has been proposed by Kundu and Gupta (J Multivar Anal 123:19-29, 2014). They derived different properties of the proposed distribution and computing the maximum likelihood estimators via the expectation-maximization algorithm. The Bayes estimators of the parameters from the BWG distribution based on the squared error loss function (symmetric) and linear-exponential (LINEX) loss function (asymmetric), using informative and non-informative gamma priors are presented. Since the Bayes estimators of the mentioned distribution with five parameters cannot be obtained in explicit forms; the Gibbs sampler procedure is opted to achieve the Bayes estimators. Markov Chain Monte Carlo (MCMC) methods are broadly used to implement and compute the Bayes estimates. The convergence of the Markov chain to a stationary distribution has also been considered in detail. The associated credible intervals, namely the highest posterior density of the unknown parameters, are also constructed. The Monte Carlo simulations are done to compare different estimates. Finally, a real data set is considered to perform for illustrative purposes.

Suggested Citation

  • Mehdi Basikhasteh & Iman Makhdoom, 2022. "Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions," 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. 13(2), pages 867-880, April.
    • Handle: RePEc:spr:ijsaem:v:13:y:2022:i:2:d:10.1007_s13198-021-01348-9
    DOI: 10.1007/s13198-021-01348-9
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    References listed on IDEAS

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    1. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    2. David D. Hanagal & Richa Sharma, 2015. "Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 24-47, January.
    3. Barreto-Souza, Wagner, 2012. "Bivariate gamma-geometric law and its induced Lévy process," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 130-145.
    4. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    5. G. Heinrich & U. Jensen, 1995. "Parameter estimation for a bivariate lifetime distribution in reliability with multivariate extensions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 49-65, December.
    6. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.
    7. Franco, Manuel & Vivo, Juana-María, 2010. "A multivariate extension of Sarhan and Balakrishnan's bivariate distribution and its ageing and dependence properties," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 491-499, March.
    8. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
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