On Dagum-Pareto mixture distribution: properties, simulation and application in insurance

Abstract

The most principal subject in actuarial science is the modeling of claims amount. There are two types of distributions associated with two types of risk. We speak of light-tailed distributions as opposed to heavy-tailed distributions or extreme value distribution. Among the distributions of the amount of heavy tail claim is: Weibull, Log-Normal, Pareto and Burr “Also named DAGUM”. Many attempts were implemented in expanding the classes of mixed and compound distributions. In this article, we present a new distribution by mixing Dagum distribution (α, λ, r) and Pareto distribution (α, λ) named Dagum-Pareto mixture distribution. Some of statistical properties of this new distribution are obtained which include reliability function, hazard function, skewness, kurtosis and quantile function. Also we use the maximum likelihood method to estimate the model parameters. A Simulation study was carried out to examine the performance and accuracy of the maximum likelihood estimates of the proposed distribution. An application of the new model to no-life insurance real data set is presented to illustrate its usefulness and applicability. In our case, it is proven that Dagum-Pareto mixture distribution provides better fit compared to others existing probability distributions using some goodness of fit measures.