On modelling insurance data by using a generalized lognormal distribution

Abstract

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occurs in practical situations. The distribution proposed is derived from the lognormal distribution, by using the Marshall and Olkin procedure. Some basic properties of this new distribution are obtained and we present situations where this new distribution correctly reflects the sample behaviour for the right tail probability. An application of the model to dental insurance data is presented and analysed in depth. We conclude that the generalized lognormal distribution proposed is a distribution that should be taken into account among other possible distributions for insurance data in which the properties of a heavy-tailed distribution are present.