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Development of a new general class of bivariate distributions based on reversed hazard rate order

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  • Yoo, Na Young
  • Lee, Hyunju
  • Cha, Ji Hwan

Abstract

Motivated by real data sets to be analyzed in this paper, we develop a new general class of bivariate distributions that can model the effect of the so-called ‘load-sharing configuration’ in a system with two components based on the reversed hazard rate. Under such load-sharing configuration, after the failure of one component, the surviving component has to shoulder extra load, which eventually results in its failure at an earlier time than what is expected under the case of independence. In the developed class of bivariate distributions, it is assumed that the residual lifetime of the remaining component is shortened according to the reversed hazard rate order. We derive the joint survival function, joint probability density function and the marginal distributions. We discuss a bivariate ageing property of the developed class of distributions. Some specific families of bivariate distributions which can be usefully applied in practice are obtained. These families of bivariate distributions are applied to some real data sets to illustrate their usefulness.

Suggested Citation

  • Yoo, Na Young & Lee, Hyunju & Cha, Ji Hwan, 2025. "Development of a new general class of bivariate distributions based on reversed hazard rate order," Computational Statistics & Data Analysis, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:csdana:v:204:y:2025:i:c:s0167947324001907
    DOI: 10.1016/j.csda.2024.108106
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    References listed on IDEAS

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    1. 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.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, July.
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    4. Paul Kabaila, 2009. "The Coverage Properties of Confidence Regions After Model Selection," International Statistical Review, International Statistical Institute, vol. 77(3), pages 405-414, December.
    5. Lee, Hyunju & Cha, Ji Hwan, 2015. "Construction of two new general classes of bivariate distributions based on stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 75-85.
    6. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
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    8. Oliveira, Ricardo P. & Achcar, Jorge A. & Mazucheli, Josmar & Bertoli, Wesley, 2021. "A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    9. 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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