ORDERING CLAIM SIZE DISTRIBUTIONS AND MIXED POISSON PROBABILITIES

We investigate various orderings between continuous distributions for severities, having the same first n moments. Such situations occur for instance when severity distributions are fitted by the method of mome nts. General results are derived which establish an ordering between s uch distributions, and these results are applied to compare the Gamma, the Inverse Gaussian and the lognormal distributions with equal means and variances. Finally, we consider the situation where such continuo us distributions are used as mixing distributions in mixed Poisson mod els for claim numbers, and show that the order properties of the mixin g distributions are inherited by the corresponding mixed Poisson distr ibutions.