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

Abstract

In actuarial science, one of the most significant subjects is the modeling of claims amount. We refer to two distinct distribution types—heavy-tailed and light-tailed distributions—that are associated with two risk categories. Weibull, Dagum, Pareto, and Log-Normal are some of the distributions of heavy tail claim amounts. Conversely, the light tail claim amounts are distributed as exponential, gamma, and exponential mixing.
This article presents the Dagum-Exponential mixture distribution, a new distribution created by combining the dagum distribution (α, ????, r) and the exponential distribution (????). It is possible to obtain the quantile function, skewness, kurtosis, reliability function, and hazard function of the Dagum-Exponential distribution. Additionally, we estimate the model parameters using the maximum likelihood method. Using an actual data set in the application highlights the significance of the new model.