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Title: | Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence An Application to Model Claim Frequency and Optimal Transformed Average Severity |
Author: | Alemany Leira, Ramon Bolancé Losilla, Catalina Rodrigo Marqués, Roberto Vernic, Raluca |
Keywords: | Risc (Assegurances) Assegurances d'automòbils Models lineals (Estadística) Variables (Matemàtica) Risk (Insurance) Automobile insurance Linear models (Statistics) Variables (Mathematics) |
Issue Date: | 1-Jan-2021 |
Publisher: | MDPI |
Abstract: | The aim of this paper is to introduce dependence between the claim frequency and the average severity of a policyholder or of an insurance portfolio using a bivariate Sarmanov distribution, that allows to join variables of different types and with different distributions, thus being a good candidate for modeling the dependence between the two previously mentioned random variables. To model the claim frequency, a generalized linear model based on a mixed Poisson distribution -like for example, the Negative Binomial (NB), usually works. However, finding a distribution for the claim severity is not that easy. In practice, the Lognormal distribution fits well in many cases. Since the natural logarithm of a Lognormal variable is Normal distributed, this relation is generalised using the Box-Cox transformation to model the average claim severity. Therefore, we propose a bivariate Sarmanov model having as marginals a Negative Binomial and a Normal Generalized Linear Models (GLMs), also depending on the parameters of the Box-Cox transformation. We apply this model to the analysis of the frequency-severity bivariate distribution associated to a pay-as-you-drive motor insurance portfolio with explanatory telematic variables. |
Note: | Reproducció del document publicat a: https://doi.org/10.3390/math9010073 |
It is part of: | Mathematics, 2021, vol. 1, num. 9 |
URI: | http://hdl.handle.net/2445/173804 |
Related resource: | https://doi.org/10.3390/math9010073 |
ISSN: | 2227-7390 |
Appears in Collections: | Articles publicats en revistes (Econometria, Estadística i Economia Aplicada) |
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