Stochastic orders based on the Laplace transform and infinitely divisible distributions

Recently, Bartoszewicz (1999, Statist. Probab. Lett. 42, 207-212), has given characterizations of stochastic orders based on the Laplace transform and obtained moment inequalities for ordered distributions. In this note, we give some relations between these orders and infinitely divisible distributions. New characterizations of the so-called -class of distributions are given.Partial orders Characterization theorem Exponential distribution Gamma distribution Laplace transform Completely monotone functions Negative moments -class