A Copula-Based Bivariate Composite Model for Modelling Claim Costs

Girish Aradhye, George Tzougas and Deepesh Bhati ()
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Girish Aradhye: Department of Statistics, Central University of Rajasthan, Ajmer 305817, India
George Tzougas: Maxwell Institute for Mathematical Sciences, Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK
Deepesh Bhati: Department of Statistics, Central University of Rajasthan, Ajmer 305817, India

Mathematics, 2024, vol. 12, issue 2, 1-17

Abstract: This paper aims to develop a new family of bivariate distributions for modelling different types of claims and their associated costs jointly in a flexible manner. The proposed bivariate distributions can be viewed as a continuous copula distribution paired with two marginals based on composite distributions. For expository purposes, the details of one of the proposed bivarite composite distributions is provided. The dependence measures for the resulting bivariate copula-based composite distribution are studied, and its fitting is compared with other bivariate composite distributions and existing bivariate distributions. The parameters of the proposed bivariate composite model are estimated via the inference functions for margins (IFM) method. The suitability of the proposed bivariate distribution is examined using two real-world insurance datasets, namely the motor third-party liability (MTPL) insurance dataset and Danish fire insurance dataset.

Keywords: copulas; dependence parameter; Gumbel copula; Inverse Weibull distribution; Inverse Burr distribution; Paralogistic distribution; Weibull distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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