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On the Bivariate Composite Gumbel–Pareto Distribution

Author

Listed:
  • Alexandra Badea

    (Doctoral School, Ovidius University of Constanta, 900527 Constanta, Romania)

  • Catalina Bolancé

    (Department of Econometrics, RISKcenter-IREA, Universitat de Barcelona, 08034 Barcelona, Spain)

  • Raluca Vernic

    (Faculty of Mathematics and Computer Science, Ovidius University of Constanta, 900527 Constanta, Romania)

Abstract

In this paper, we propose a bivariate extension of univariate composite (two-spliced) distributions defined by a bivariate Pareto distribution for values larger than some thresholds and by a bivariate Gumbel distribution on the complementary domain. The purpose of this distribution is to capture the behavior of bivariate data consisting of mainly small and medium values but also of some extreme values. Some properties of the proposed distribution are presented. Further, two estimation procedures are discussed and illustrated on simulated data and on a real data set consisting of a bivariate sample of claims from an auto insurance portfolio. In addition, the risk of loss in this insurance portfolio is estimated by Monte Carlo simulation.

Suggested Citation

  • Alexandra Badea & Catalina Bolancé & Raluca Vernic, 2022. "On the Bivariate Composite Gumbel–Pareto Distribution," Stats, MDPI, vol. 5(4), pages 1-22, October.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:55-969:d:943861
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    References listed on IDEAS

    as
    1. Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
    2. Daeyoung Kim & Bruce Lindsay, 2015. "Empirical identifiability in finite mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 745-772, August.
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