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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
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    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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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2009)
    Issue (Month): 4 (February)
    Pages: 956-965

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    Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:956-965

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    1. Hanagal David D., 2005. "A Bivariate Weibull Regression Model," Economic 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, vol. 55(4), pages 817-830, December.
    3. David Hanagal, 2006. "Bivariate Weibull regression model based on censored samples," Statistical Papers, Springer, vol. 47(1), pages 137-147, January.
    4. Patra, Kaushik & Dey, Dipak K., 1999. "A multivariate mixture of Weibull distributions in reliability modeling," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 225-235, November.
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    Cited by:
    1. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    2. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    3. 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.
    4. 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.
    5. 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.
    6. Christian Hering & Jan-Frederik Mai, 2012. "Moment-based estimation of extendible Marshall-Olkin copulas," Metrika, Springer, vol. 75(5), pages 601-620, July.


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