Financial and actuarial properties of the Beta-Pareto as a Long-Tail Distribution

Abstract

Undoubtedly, the single parameter Pareto distribution is one of the most attractive distri- bution in statistics; a power-law probability distribution that is found in a large number of real-world situations inside and outside the field of economics. Furthermore, it is usually used as a basis for ex- cess of loss quotations as it gives a pretty good description of the random behaviour of large losses. In this paper, we provide properties of the Beta-Pareto distribution which can be useful in Economics, and in Financial and Actuarial fields, mainly related to the analysis of the tail of the distribution that makes it a candidate model for fitting actuarial data with extreme observations. As empirical applications two well-known data sources considered in general insurance are used to account for the suitability of the model.