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A multivariate mixture of Weibull distributions in reliability modeling

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  • Patra, Kaushik
  • Dey, Dipak K.

Abstract

A new class of multivariate distribution is derived where each component is a mixture of Weibull distribution. The approach in this paper is based on the introduction of an exponentially distributed latent random variable. The new class includes several multivariate and bivariate models including Marshall and Olkin type. The moment generating function and, hence, the correlation structure is obtained for the bivariate situation. The distribution of the minimum in a competing risk framework is discussed and various other properties including correlation structures are investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:3:p:225-235
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    References listed on IDEAS

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    1. Jye Lu & Gouri Bhattacharyya, 1990. "Some new constructions of bivariate Weibull models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 543-559, September.
    2. Lee, Larry, 1979. "Multivariate distributions having Weibull properties," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 267-277, June.
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    Cited by:

    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. Manuel Franco & Narayanaswamy Balakrishnan & Debasis Kundu & Juana-María Vivo, 2014. "Generalized mixtures of Weibull components," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 515-535, September.
    3. Franco, Manuel & Vivo, Juana-María, 2009. "Constraints for generalized mixtures of Weibull distributions with a common shape parameter," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1724-1730, August.
    4. 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.
    5. Patrick Mair & Marcus Hudec, 2009. "Multivariate Weibull mixtures with proportional hazard restrictions for dwell‐time‐based session clustering with incomplete data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(5), pages 619-639, December.
    6. 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.
    7. 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.
    8. Daniel Villanueva & Andrés Feijóo & José L. Pazos, 2013. "Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment," Resources, MDPI, vol. 2(3), pages 1-15, September.

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