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On bivariate Weibull-Geometric distribution

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  • Kundu, Debasis
  • Gupta, Arjun K.

Abstract

Marshall and Olkin (1997) [14] provided a general method to introduce a parameter into a family of distributions and discussed in details about the exponential and Weibull families. They have also briefly introduced the bivariate extension, although not any properties or inferential issues have been explored, mainly due to analytical intractability of the general model. In this paper we consider the bivariate model with a special emphasis on the Weibull distribution. We call this new distribution as the bivariate Weibull-Geometric distribution. We derive different properties of the proposed distribution. This distribution has five parameters, and the maximum likelihood estimators cannot be obtained in closed form. We propose to use the EM algorithm, and it is observed that the implementation of the EM algorithm is quite straightforward. Two data sets have been analyzed for illustrative purposes, and it is observed that the new model and the proposed EM algorithm work quite well in these cases.

Suggested Citation

  • Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:19-29
    DOI: 10.1016/j.jmva.2013.08.004
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Kundu, Debasis & Gupta, Rameshwar D., 2009. "Bivariate generalized exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 581-593, April.
    4. 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.
    5. 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.
    6. 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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    Cited by:

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    2. Raj Kamal Maurya & Yogesh Mani Tripathi & Chandrakant Lodhi & Manoj Kumar Rastogi, 2019. "On a generalized Lomax 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. 10(5), pages 1091-1104, October.
    3. 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.
    4. Na Young Yoo & Ji Hwan Cha, 2024. "General classes of bivariate distributions for modeling data with common observations," Statistical Papers, Springer, vol. 65(8), pages 5219-5238, October.

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