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A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters

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  • Indranil Ghosh

    (University of North Carolina)

  • Osborne Banks

    (University of North Carolina)

Abstract

Several variants of the classical bivariate and multivariate generalized Pareto distributions have been discussed and studied in the literature (see Arnold (1983, Stat. Prob. Lett. 17: 361–368, 1993, 2015), Arnold and Laguna (1977), Ali and Nadarajah (2007), Rootzen and Tajvidi (2006) and the references cited therein). Ali and Nadarajah (2007) studied a truncated version of the most popular long-tailed generalized bivariate Pareto distribution (GBPD, henceforth, in short) involving six parameters. However, not much discussion exists in the current literature on the structural properties as well as on the dependence structure among the parameters in this model. In this paper we re-visit the GBPD and discuss several other new properties. In addition, we study the shape of GBPD for varying choices of the model parameters and subsequently study their interdependence. Also, we provide copula based construction of GBPD and discuss the associated local dependence measures.

Suggested Citation

  • Indranil Ghosh & Osborne Banks, 2021. "A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 575-604, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00224-z
    DOI: 10.1007/s13571-020-00224-z
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    References listed on IDEAS

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    1. P. G. Sankaran & N. Unnikrishnan Nair & Preethi John, 2014. "A family of bivariate Pareto distributions," Statistica, Department of Statistics, University of Bologna, vol. 74(2), pages 199-215.
    2. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose María, 1993. "Multivariate distributions with generalized Pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 361-368, August.
    3. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    4. Colangelo, Antonio & Hu, Taizhong & Shaked, Moshe, 2008. "Conditional orderings and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 358-371, March.
    5. Jones, M. C., 1998. "Constant Local Dependence," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 148-155, February.
    6. Falk, Michael & Guillou, Armelle, 2008. "Peaks-over-threshold stability of multivariate generalized Pareto distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 715-734, April.
    7. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
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