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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:
It is part of: Mathematics, 2021, vol. 1, num. 9
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ISSN: 2227-7390
Appears in Collections:Articles publicats en revistes (Econometria, Estadística i Economia Aplicada)

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