On the Bivariate Composite Gumbel-Pareto Distribution
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...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/194380 |
| Acesso em linha: | https://hdl.handle.net/2445/194380 |
| Access Level: | acceso abierto |
| Palavra-chave: | Variables (Matemàtica) Teoria de distribucions (Anàlisi funcional) Teoria de l'estimació Mesures de probabilitats Gestió del risc Variables (Mathematics) Theory of distributions (Functional analysis) Estimation theory Probability measures Risk management |
| Resumo: | 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 |
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