Partly Divisible Probability Distributions

Abstract

Given a probability distribution $\mu$ a set $\Lambda (\mu )$ of positive real numbers is introduced, so that $\Lambda (\mu )$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu )$ are described and examples of probability distributions are given, which exhibit the existence of a continuum of situations interpolating the extreme cases of infinitely and minimally divisible probability distributions.

11 pages