Odd Pareto families of distributions for modeling loss payment data

Abstract

A three-parameter generalization of the Pareto distribution is presented with density function having a flexible upper tail in modeling loss payment data. This generalized Pareto distribution will be referred to as the Odd Pareto distribution since it is derived by considering the distributions of the odds of the Pareto and inverse Pareto distributions. Basic properties of the Odd Pareto distribution (OP) are studied. Model parameters are estimated using both modified and regular maximum likelihood methods. Simulation studies are conducted to compare the OP with the exponentiated Pareto, Burr, and Kumaraswamy distributions using two different test statistics based on the ml method. Furthermore, two examples from the Norwegian fire insurance claims data-set are provided to illustrate the upper tail flexibility of the distribution. Extensions of the Odd Pareto distribution are also considered to improve the fitting of data.