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Approximations for Bivariate Extreme Values

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Abstract

We study the tail behavior of distributions in the domain of attraction of bivariate extreme value distributions (this includes bivariate extreme value distributions themselves). We provide results on finite approximations of the tail behavior and its analytical shape. The results could form a basis to improve current statistical modeling of bivariate extreme values.

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References

  • Clayton, D.G., “A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence,” Biometrika 65, 141-145, (1978).

    Google Scholar 

  • Coles, S.G. and Tawn, J.A., “Modeling extreme multivariate events,” Journal of the Royal Statistical Society B 53, 377-392, (1991).

    Google Scholar 

  • Gumbel, E.J., “Bivariate exponential distributions,” Journal of the American Statistical Association 55, 698-707, (1960).

    Google Scholar 

  • Joe, H., “Families of min-stable multivariate exponential and multivariate extreme value distributions,” Statistics and Probability Letters 9, 75-81, (1990).

    Google Scholar 

  • Joe, H., Smith, R.L., and Weissman, I., “Bivariate threshold methods for extremes,” Journal of the Royal Statistical Society B 54, 171-183, (1992).

    Google Scholar 

  • Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate extreme values,” Biometrika 83, 169-187, (1996).

    Google Scholar 

  • Morgenstern, D., “Einfache beispiele zweidimensionaler verteilungen,” Mitteilings-blatt fur Mathematische Statistik 8, 234-235, (1956).

    Google Scholar 

  • Oakes, D., “A model for association in bivariate survival data,” Journal of the Royal Statistical Society B 44, 414-422, (1982).

    Google Scholar 

  • Oakes, D., “Semiparametric inference in a model for association in bivariate survival data,” Biometrika 73, 353-361, (1986).

    Google Scholar 

  • Resnick, S.I., Extreme values, regular variation and point processes, New York: Springer Verlag, 1987.

    Google Scholar 

  • Smith, R.L., Tawn, J.A. and Coles, S.G., “Markov chain models for threshold exceedances,” Biometrika 84, 249-268, (1997).

    Google Scholar 

  • Tawn, J.A., “Bivariate extreme value theory: Models and estimation,” Biometrika 75, 397-415, (1988).

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom;

    S. Nadarajah

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  1. S. Nadarajah
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Nadarajah, S. Approximations for Bivariate Extreme Values. Extremes 3, 87–98 (2000). https://doi.org/10.1023/A:1009927321376

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  • DOI: https://doi.org/10.1023/A:1009927321376

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