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A new extreme value copula and new families of univariate distributions based on Freund’s exponential model

Author

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  • Guzmics Sándor

    (University of Vienna. Department of Statistics and Operations Research (DSOR), Oskar Morgenstern Platz 1, A-1090 Wien-Vienna, Austria)

  • Pflug Georg Ch.

    (DSOR and International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria)

Abstract

The use of the exponential distribution and its multivariate generalizations is extremely popular in lifetime modeling. Freund’s bivariate exponential model (1961) is based on the idea that the remaining lifetime of any entity in a bivariate system is shortened when the other entity defaults. Such a model can be quite useful for studying systemic risk, for instance in financial systems. Guzmics and Pflug (2019) revisited Freund’s model, deriving the corresponding bivariate copula and examined some characteristics of it; furthermore, we opened the door for a multivariate setting. Now we present further investigations in the bivariate model: we compute the tail dependence coefficients, we examine the marginal and joint distributions of the componentwise maxima, which leads to an extreme value copula, which – to the best of our knowledge – has not been investigated in the literature yet. The original bivariate model of Freund has been extended to more variables by several authors. We also turn to the multivariate setting, and our focus is different from that of the previous generalizations, and therefore it is novel: examining the distribution of the sum and of the average of the lifetime variables (provided that the shock parameters are all the same) leads to new families of univariate distributions, which we call Exponential Gamma Mixture Type I and Type II (EGM) distributions. We present their basic properties, we provide asymptotics for them, and finally we also provide the limiting distribution for the EGM Type II distribution.

Suggested Citation

  • Guzmics Sándor & Pflug Georg Ch., 2020. "A new extreme value copula and new families of univariate distributions based on Freund’s exponential model," Dependence Modeling, De Gruyter, vol. 8(1), pages 330-360, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:330-360:n:7
    DOI: 10.1515/demo-2020-0018
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    References listed on IDEAS

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    1. Stefan Hochrainer-Stigler & Juraj Balkovič & Kadri Silm & Anna Timonina-Farkas, 2019. "Large scale extreme risk assessment using copulas: an application to drought events under climate change for Austria," Computational Management Science, Springer, vol. 16(4), pages 651-669, October.
    2. Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
    3. Brenden Jongman & Stefan Hochrainer-Stigler & Luc Feyen & Jeroen C. J. H. Aerts & Reinhard Mechler & W. J. Wouter Botzen & Laurens M. Bouwer & Georg Pflug & Rodrigo Rojas & Philip J. Ward, 2014. "Increasing stress on disaster-risk finance due to large floods," Nature Climate Change, Nature, vol. 4(4), pages 264-268, April.
    4. Norros, Ilkka, 1985. "Systems weakend by failures," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 181-196, September.
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