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Article

On the Bivariate Composite Gumbel–Pareto Distribution

1
Doctoral School, Ovidius University of Constanta, 900527 Constanta, Romania
2
Department of Econometrics, RISKcenter-IREA, Universitat de Barcelona, 08034 Barcelona, Spain
3
Faculty of Mathematics and Computer Science, Ovidius University of Constanta, 900527 Constanta, Romania
*
Author to whom correspondence should be addressed.
Academic Editor: Wei Zhu
Stats 2022, 5(4), 948-969; https://doi.org/10.3390/stats5040055
Received: 31 August 2022 / Revised: 30 September 2022 / Accepted: 13 October 2022 / Published: 16 October 2022
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 bivariate composite (two-spliced) distribution; Gumbel’s bivariate exponential distribution; bivariate Pareto of the first kind distribution; maximum likelihood estimation procedure; risk of loss
MDPI and ACS Style

Badea, A.; Bolancé, C.; Vernic, R. On the Bivariate Composite Gumbel–Pareto Distribution. Stats 2022, 5, 948-969. https://doi.org/10.3390/stats5040055

AMA Style

Badea A, Bolancé C, Vernic R. On the Bivariate Composite Gumbel–Pareto Distribution. Stats. 2022; 5(4):948-969. https://doi.org/10.3390/stats5040055

Chicago/Turabian Style

Badea, Alexandra, Catalina Bolancé, and Raluca Vernic. 2022. "On the Bivariate Composite Gumbel–Pareto Distribution" Stats 5, no. 4: 948-969. https://doi.org/10.3390/stats5040055

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