A suitable alternative to the Pareto distribution

Abstract

Undoubtedly, the single parameter Pareto distribution is one of the most attractive distribution in statistics; a power law probability distribution 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 excess of loss quotations as it gives a pretty good description of the random behaviour of large losses. In this paper, we introduce a distribution which can be considered as alternative to the single parameter Pareto distribution. A comprehensive treatment of its mathematical properties is considered with relevant emphasis on results concerning insurance. Additionally, estimation by the method of moments and maximum likelihood is discussed. Then, an analysis of estimation performance is carried out. Finally, the performance of the model is examined by using two examples of real claims data.