Abstract
This article presents the Exponential–Generalized Inverse Gaussian regression model with varying dispersion and shape. The EGIG is a general distribution family which, under the adopted modelling framework, can provide the appropriate level of flexibility to fit moderate costs with high frequencies and heavy-tailed claim sizes, as they both represent significant proportions of the total loss in non-life insurance. The model’s implementation is illustrated by a real data application which involves fitting claim size data from a European motor insurer. The maximum likelihood estimation of the model parameters is achieved through a novel Expectation Maximization (EM)-type algorithm that is computationally tractable and is demonstrated to perform satisfactorily.
Highlights
In the recent literature, in various fields of research such as seismology, biology, genetics, econometrics and insurance, an interest has been developed in modelling rightskewed data which are dominated by large values
The Egig function was recently used by Tzougas (2020) to compute the posterior expectations at the E-Step of the EM algorithm, which was developed to estimate the parameters of the Poisson–Inverse Gamma regression model with varying dispersion
We proposed an EM-type algorithm to estimate the parameters of the Exponential–Generalized Inverse Gaussian (EGIG) regression model with varying dispersion and shape
Summary
In various fields of research such as seismology, biology, genetics, econometrics and insurance, an interest has been developed in modelling rightskewed data which are dominated by large values. In Tzougas and Karlis (2020), the authors calibrated heavy-tailed insurance losses using a class of mixed Exponential Regression models with varying dispersion Their proposed class of models extends the setup of many well-known two parameter mixed Exponential distributions, such as the classic Exponential–Inverse Gamma—namely Pareto—, the Exponential–Inverse Gaussian (EIG) distributions and the Exponential–Lognormal (ELN) distribution, which was recently considered in Tzougas et al (2020). Inverse Gamma), Exponential–Inverse Exponential, Exponential–Inverse Chi Squared and Exponential–Scaled Inverse Chi Squared distributions, depending on the estimated values of the dispersion and shape parameters which are modelled as functions of risk factors This can be regarded as a very useful property since, as is well known, real non-life insurance datasets are a mix of moderate and large claim amounts.
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