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Construction of asymmetric copulas and its application in two-dimensional reliability modelling

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  • Wu, Shaomin

Abstract

Copulas offer a useful tool in modelling the dependence among random variables. In the literature, most of the existing copulas are symmetric while data collected from the real world may exhibit asymmetric nature. This necessitates developing asymmetric copulas that can model such data. In the meantime, existing methods of modelling two-dimensional reliability data are not able to capture the tail dependence that exists between the pair of age and usage, which are the two dimensions designated to describe product life. This paper proposes a new method of constructing asymmetric copulas, discusses the properties of the new copulas, and applies the method to fit two-dimensional reliability data that are collected from the real world.

Suggested Citation

  • Wu, Shaomin, 2014. "Construction of asymmetric copulas and its application in two-dimensional reliability modelling," European Journal of Operational Research, Elsevier, vol. 238(2), pages 476-485.
  • Handle: RePEc:eee:ejores:v:238:y:2014:i:2:p:476-485
    DOI: 10.1016/j.ejor.2014.03.016
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    References listed on IDEAS

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    1. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    2. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    3. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
    4. repec:eee:reensy:v:106:y:2012:i:c:p:160-164 is not listed on IDEAS
    5. Zhang, Ming-Heng, 2008. "Modelling total tail dependence along diagonals," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 73-80, February.
    6. repec:eee:reensy:v:116:y:2013:i:c:p:126-134 is not listed on IDEAS
    7. Ye, Wuyi & Liu, Xiaoquan & Miao, Baiqi, 2012. "Measuring the subprime crisis contagion: Evidence of change point analysis of copula functions," European Journal of Operational Research, Elsevier, vol. 222(1), pages 96-103.
    8. Wu, Shaomin & Akbarov, Artur, 2011. "Support vector regression for warranty claim forecasting," European Journal of Operational Research, Elsevier, vol. 213(1), pages 196-204, August.
    9. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    10. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650.
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    Citations

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    Cited by:

    1. Antonio Dalessandro & Gareth W. Peters, 2015. "Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators," Papers 1502.06349, arXiv.org.
    2. Rychlik, Tomasz, 2017. "Evaluations of quantiles of system lifetime distributions," European Journal of Operational Research, Elsevier, vol. 256(3), pages 935-944.
    3. repec:eee:reensy:v:142:y:2015:i:c:p:326-333 is not listed on IDEAS
    4. repec:eee:ejores:v:266:y:2018:i:1:p:269-277 is not listed on IDEAS
    5. Siburg, Karl Friedrich & Stehling, Katharina & Stoimenov, Pavel A. & Weiß, Gregor N.F., 2016. "An order of asymmetry in copulas, and implications for risk management," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 241-247.
    6. Elena Di Bernardino & Didier Rullière, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Working Papers hal-01147778, HAL.
    7. repec:eee:reensy:v:153:y:2016:i:c:p:75-87 is not listed on IDEAS
    8. repec:eee:ejores:v:267:y:2018:i:2:p:513-522 is not listed on IDEAS
    9. repec:eee:proeco:v:196:y:2018:i:c:p:101-112 is not listed on IDEAS

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