Distributions of class Lα

Abstract

AbstractLα (0 ≦ α ≦ 1) is a class of infinitely divisible distributions defined by restricting the measure in the Levy-Khinchin formula to a special form. When α = 1, Lα is just the classical class L. Several properties for Lα classes, which are similar to the most important properties for the class L, are established. Also, a conjecture of Wolfe about unimodality of some Lα distributions is disproved by giving a counterexample