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Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm

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  • Kundu, Debasis
  • Dey, Arabin Kumar

Abstract

In this paper we consider the Marshall-Olkin bivariate Weibull distribution. The Marshall-Olkin bivariate Weibull distribution is a singular distribution, whose both the marginals are univariate Weibull distributions. This is a generalization of the Marshall-Olkin bivariate exponential distribution. The cumulative joint distribution of the Marshall-Olkin bivariate Weibull distribution is a mixture of an absolute continuous distribution function and a singular distribution function. This distribution has four unknown parameters and it is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. In this paper we discuss about the computation of the maximum likelihood estimators of the unknown parameters using EM algorithm. We perform some simulations to see the performances of the EM algorithm and re-analyze one data set for illustrative purpose.

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  • Kundu, Debasis & Dey, Arabin Kumar, 2009. "Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 956-965, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:956-965
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    References listed on IDEAS

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    1. Hanagal David D., 2005. "A Bivariate Weibull Regression Model," Stochastics and Quality Control, De Gruyter, vol. 20(1), pages 143-150, January.
    2. Dimitris Karlis, 2003. "ML estimation for multivariate shock models via an EM algorithm," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 817-830, December.
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    3. Kundu, Debasis & Gupta, Arjun K., 2013. "Bayes estimation for the Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 271-281.
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    7. Nandi, Swagata & Dewan, Isha, 2010. "An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1559-1569, June.
    8. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    9. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    10. El-Sayed A. El-Sherpieny & Ehab M. Almetwally & Hiba Z. Muhammed, 2023. "Bayesian and Non-Bayesian Estimation for the Parameter of Bivariate Generalized Rayleigh Distribution Based on Clayton Copula under Progressive Type-II Censoring with Random Removal," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1205-1242, August.
    11. Christian Hering & Jan-Frederik Mai, 2012. "Moment-based estimation of extendible Marshall-Olkin copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 601-620, July.
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    13. Rakesh Ranjan & Vastoshpati Shastri, 2019. "Posterior and predictive inferences for Marshall Olkin bivariate Weibull distribution via Markov chain Monte Carlo methods," 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. 10(6), pages 1535-1543, December.
    14. Li, Yang & Sun, Jianguo & Song, Shuguang, 2012. "Statistical analysis of bivariate failure time data with Marshall–Olkin Weibull models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2041-2050.
    15. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    16. Yuan Ma & Wenhao Gui, 2021. "Competing Risks Step-Stress Model with Lagged Effect under Gompertz Distribution," Mathematics, MDPI, vol. 9(24), pages 1-26, December.
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    18. Raffaella Calabrese & Silvia Osmetti, 2014. "Modelling cross-border systemic risk in the European banking sector: a copula approach," Papers 1411.1348, arXiv.org.

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