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Multivariate distributions having Weibull properties

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  • Lee, Larry

Abstract

Random variables X1 ,..., Xn are said to have a joint distribution with Weibull minimums after arbitrary scaling if mini(aiXi) has a one dimensional Weibull distribution for arbitrary constants ai > 0, I = 1,..., n. Some properties of this class are demonstrated, and some examples are given which show the existence of a number of distributions belonging to the class. One of the properties is found to be useful for computing component reliability importance. The class is seen to contain an absolutely continuous Weibull distribution which can be generated from independent uniform and gamma distributions.

Suggested Citation

  • Lee, Larry, 1979. "Multivariate distributions having Weibull properties," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 267-277, June.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:2:p:267-277
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    Citations

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    Cited by:

    1. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    2. Hanagal David, 2005. "Weibull Extension of a Bivariate Exponential Regression Model," Stochastics and Quality Control, De Gruyter, vol. 20(2), pages 247-253, January.
    3. Nadarajah Saralees & Kotz Samuel, 2006. "Determination of Software Reliability based on Multivariate Exponential, Lomax and Weibull Models," Monte Carlo Methods and Applications, De Gruyter, vol. 12(5), pages 447-459, November.
    4. Yeh, Hsiaw-Chan, 2009. "Multivariate semi-Weibull distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1634-1644, September.
    5. Weekes, S.M. & Tomlin, A.S., 2014. "Comparison between the bivariate Weibull probability approach and linear regression for assessment of the long-term wind energy resource using MCP," Renewable Energy, Elsevier, vol. 68(C), pages 529-539.
    6. Roy, Dilip & Mukherjee, S. P., 1998. "Multivariate Extensions of Univariate Life Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 72-79, October.
    7. Feijóo, Andrés & Villanueva, Daniel & Pazos, José Luis & Sobolewski, Robert, 2011. "Simulation of correlated wind speeds: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(6), pages 2826-2832, August.
    8. Hanagal David D., 2006. "Weibull Extension of Bivariate Exponential Regression Model with Gamma Frailty for Survival Data," Stochastics and Quality Control, De Gruyter, vol. 21(2), pages 261-270, January.
    9. Wang, Antai & Oakes, David, 2008. "Some properties of the Kendall distribution in bivariate Archimedean copula models under censoring," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2578-2583, November.
    10. David Hanagal, 2009. "Weibull extension of bivariate exponential regression model with different frailty distributions," Statistical Papers, Springer, vol. 50(1), pages 29-49, January.
    11. 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.
    12. Feijóo, Andrés & Villanueva, Daniel, 2016. "Assessing wind speed simulation methods," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 473-483.
    13. 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.
    14. Hansjörg Albrecher & Mogens Bladt & Jorge Yslas, 2022. "Fitting inhomogeneous phase‐type distributions to data: the univariate and the multivariate case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 44-77, March.
    15. Lee, Hyunju & Cha, Ji Hwan, 2014. "On construction of general classes of bivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 151-159.

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