On the Bivariate Composite Gumbel–Pareto Distribution

Alexandra Badea, Catalina Bolancé and Raluca Vernic ()
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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

Stats, 2022, vol. 5, issue 4, 1-22

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.

Keywords: bivariate composite (two-spliced) distribution; Gumbel’s bivariate exponential distribution; bivariate Pareto of the first kind distribution; maximum likelihood estimation procedure; risk of loss (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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