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Published version

Publication date

2022-10

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cc-by (c) Badea, Alexandra et al., 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/194380

On the Bivariate Composite Gumbel-Pareto Distribution

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https://doi.org/10.3390/stats5040055

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

Subject

Variables (Matemàtica), Teoria de distribucions (Anàlisi funcional), Teoria de l'estimació, Mesures de probabilitats, Gestió del risc

Subject (English)

Variables (Mathematics), Theory of distributions (Functional analysis), Estimation theory, Probability measures, Risk management

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Articles publicats en revistes (Econometria, Estadística i Economia Aplicada)

Citation

BADEA, Alexandra, BOLANCÉ LOSILLA, Catalina and VERNIC, Raluca. On the Bivariate Composite Gumbel-Pareto Distribution. Stats. 2022. Vol. 5, num. 4, pags. 948-969. ISSN 2571-905X. [consulted: 12 of June of 2026]. Available at: https://hdl.handle.net/2445/194380

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