The Harris Lomax Distribution. A New Probability Distribution with Application on Insurance Data

Based on the method proposed by Aly and Benkherouf (2011) to generate new distributionfamilies, a new distribution based on the Lomax (Lomax, 1954) and Harris (Harris, 1948)distributions is defined and analyzed in this article. The proposed distribution, called theHarris Lomax distribution, can be considered a generalization of the Lomax distributionand another alternative to model random variables with support in R + . The Harris Lomaxdistribution allows us to model data that show an increasing or decreasing failure rate.Other important mathematical and statistical properties are discussed, such as the quantilefunction, moments, moment generating function, order statistics and Rényi entropy. Themaximum likelihood method is used to estimate the model parameters and a simulationstudy is presented to study its performance. Two applications on real data are performed.One presents insurer’s claims data, which consists of the amount paid to settle a claim, theother presents remission times to remission in cancer patients, to illustrate the flexibilityof the proposed distribution compared to other existing distributions.