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Multivariate flexible Pareto model: Dependency structure, properties and characterizations

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  • Chiragiev, Arthur
  • Landsman, Zinoviy

Abstract

The classical multivariate Pareto model, which was referred to by Arnold [Arnold, B.C., 1983. Pareto Distributions. International Co-operative Publishing House], and is used to fit heavy tailed random variables, has serious disadvantages. First, each of its marginals has the same distribution up to location and scale parameters. Secondly, this model has a rigid dependence structure. Furthermore, the independent Pareto marginals do not belong to this model. In this paper, we introduce two multivariate models, whose marginals have different shape parameters and a more flexible dependence structure. Moreover, the independent Pareto marginals model is a special case of one of the suggested models. We also discuss regression and a measure of dependence for these models, along with some relevant inferences. The paper concludes with a numerical study.

Suggested Citation

  • Chiragiev, Arthur & Landsman, Zinoviy, 2009. "Multivariate flexible Pareto model: Dependency structure, properties and characterizations," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1733-1743, August.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:16:p:1733-1743
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    References listed on IDEAS

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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, September.
    2. Mathai, A. M. & Moschopoulos, P. G., 1991. "On a multivariate gamma," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 135-153, October.
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    4. Pycke, Jean-Renaud, 2003. "Multivariate extensions of the Anderson-Darling process," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 387-399, July.
    5. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
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    1. Sarabia, José María & Gómez-Déniz, Emilio & Prieto, Faustino & Jordá, Vanesa, 2016. "Risk aggregation in multivariate dependent Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 154-163.
    2. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    3. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Distributional properties," Papers 1607.04739, arXiv.org.
    4. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Distributional properties," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 56-68.
    5. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    6. Asimit, Alexandru V. & Furman, Edward & Vernic, Raluca, 2010. "On a multivariate Pareto distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 308-316, April.

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