On the Usefulness of the Logarithmic Skew Normal Distribution for Describing Claims Size Data

Abstract

In this paper, the three-parameter skew lognormal distribution is proposed to model actuarial data concerning losses. This distribution yields a satisfactory fit to empirical data in the whole range of the empirical distribution as compared to other distributions used in the actuarial statistics literature. To the best of our knowledge, this distribution has not been used in insurance context and it might be suitable for computing reinsurance premiums in situations where the right tail of the empirical distribution plays an important role. Furthermore, a regression model can be simply derived to explain the response variable as a function of a set of explanatory variables.