PARAMETRIC DISTRIBUTION FAMILIES USEFUL FOR MODELLING NON-LIFE INSURANCE PAYMENTS DATA. TAIL BEHAVIOUR

The present paper describes a series of parametric distributions used for modeling non-life insurance payments data. Of those listed, special attention is paid to the transformed Beta distribution family. This distribution as well as those which are obtained from it (special cases of four-parameter transformed Beta distribution) are used in the modeling of high costs, or even extreme ones. In the literature it follows the tail behaviour of distributions depending on the parameters, because the insurance payments data are tipically highly positively skewed and distributed with large upper tails. In the paper is described the tail behavior of the distribution in the left and right side respectively, and deduced from it, a general case. There are also some graphs of probability density function for one of the transformed Beta family members, which comes to reinforce the comments made.