The Lomax regression model with residual analysis: an application to insurance data

Abstract

In this paper, we introduce a new regression model, called Lomax regression model, as an alternative to the gamma regression model. The maximum-likelihood method is used to estimate the unknown parameters of the proposed model, and the finite sample performance of the maximum-likelihood estimation method is evaluated by means of the Monte-Carlo simulation study. The randomized quantile residuals are used to check the adequacy of the fitted model. The insurance data are analyzed to demonstrate the usefulness of the proposed regression model against the gamma regression model.

Keywords: 62E15; Gamma regression; Lomax distribution; heteroscedasticity; insurance loss; maximum likelihood.