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The pairwise beta distribution: A flexible parametric multivariate model for extremes

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  • Cooley, Daniel
  • Davis, Richard A.
  • Naveau, Philippe

Abstract

We present a new parametric model for the angular measure of a multivariate extreme value distribution. Unlike many parametric models that are limited to the bivariate case, the flexible model can describe the extremes of random vectors of dimension greater than two. The novel construction method relies on a geometric interpretation of the requirements of a valid angular measure. An advantage of this model is that its parameters directly affect the level of dependence between each pair of components of the random vector, and as such the parameters of the model are more interpretable than those of earlier parametric models for multivariate extremes. The model is applied to air quality data and simulated spatial data.

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  • Cooley, Daniel & Davis, Richard A. & Naveau, Philippe, 2010. "The pairwise beta distribution: A flexible parametric multivariate model for extremes," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2103-2117, October.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2103-2117
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    Cited by:

    1. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    2. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.
    3. Goix, Nicolas & Sabourin, Anne & Clémençon, Stephan, 2017. "Sparse representation of multivariate extremes with applications to anomaly detection," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 12-31.
    4. Mourahib, Anas & Kiriliouk, Anna & Segers, Johan, 2023. "Multivariate generalized Pareto distributions along extreme directions," LIDAM Discussion Papers ISBA 2023034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Nadarajah, Saralees, 2013. "Expansions for bivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 744-752.
    6. de Carvalho, Miguel & Oumow, Boris & Segers, Johan & WarchoÅ‚, MichaÅ‚, 2012. "A Euclidean likelihood estimator for bivariate tail dependence," LIDAM Discussion Papers ISBA 2012013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Hu, Shuang & Peng, Zuoxiang & Segers, Johan, 2022. "Modelling multivariate extreme value distributions via Markov trees," LIDAM Discussion Papers ISBA 2022021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Simpson, Emma S. & Wadsworth, Jennifer L. & Tawn, Jonathan A., 2021. "A geometric investigation into the tail dependence of vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    9. Papastathopoulos, Ioannis & Strokorb, Kirstin, 2016. "Conditional independence among max-stable laws," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 9-15.
    10. Segers, Johan, 2012. "Max-Stable Models For Multivariate Extremes," LIDAM Discussion Papers ISBA 2012011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Sabourin, Anne & Naveau, Philippe, 2014. "Bayesian Dirichlet mixture model for multivariate extremes: A re-parametrization," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 542-567.

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