Box-Cox transformation on the framework of Sarmanov Distribution

Abstract

It is known that in some cases the classical assumption of independence between claim frequency and claim severity does not hold in the collective model. Nowadays exists an increasing interest in models which capture this dependence. In this work we propose to consider the Sarmanov distribution as a bivariate model which captures this kind of dependence. On the other hand, Box-Cox family of transformations are widely used in data analysis to eliminate skewness and other distributional features that complicate analysis, transforming the original data into a Normal distributed sample. We also consider the average claim severity distributed as a Box-Cox back transformed from a Normal distribution in the framework of Sarmanov bivariate distribution. Assuming that the diferences between a Normal distribution and claim severity distribution can be explained in terms of a Box-Cox transformation. More over, we propose a maximum likelihood estimation procedure adapted to this Box-Cox transformed bivariate Sarmanov distribution to estimate the parameters of the model.