Abstract
In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the loggamma distribution. A comprehensive exploration of its statistical properties and theoretical results related to insurance are provided. Estimation is performed by using the method of log-moments and maximum likelihood. Also, as the modal value of this distribution is expressed in closed-form, composite parametric models are easily obtained by a mode matching procedure. The performance of both the mixture Pareto-loggamma distribution and composite models are tested by employing different claims datasets.
Highlights
In general insurance, pricing is one of the most complex processes and is no easy task but a long-drawn exercise involving the crucial step of modeling past claim data
This family is derived by using of an exponential transformation of the generalized Lindley distribution
We have proposed a new heavy-tailed class of distribution, that is obtained by using an exponential transformation of the generalized Lindley distribution
Summary
In general insurance, pricing is one of the most complex processes and is no easy task but a long-drawn exercise involving the crucial step of modeling past claim data. Different approaches to derive new classes of probability distributions that could provide more flexibility when modelling large losses has been added to the literature This includes transformation method, the composition of two or more distributions, compounding of distributions or a finite mixture of distributions among other methodologies. A probabilistic family, the mixture Pareto-loggamma distribution, which belongs to the heavy-tailed class of probabilistic models is introduced This family is derived by using of an exponential transformation of the generalized Lindley distribution. Calderín-Ojeda and Kwok (2016) introduced a new class of composite model using mode-matching procedure They derived composite models using lognormal and Weibull distributions with a Stoppa model, a generalization of the Pareto distribution.
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