Mutant Number Laws and Infinite Divisibility

Abstract

Concepts of infinitely divisible distributions are reviewed and applied to mutant number distributions derived from the Lea-Coulson and other models which describe the Luria-Delbrück fluctuation test. A key finding is that mutant number distributions arising from a generalised Lea-Coulson model for which normal cell growth is non-decreasing are unimodal. An integral criterion is given which separates the cases of a mode at the origin, or not.

Keywords

• infinite divisibility
• Bernstein function
• self-decomposability
• generalised gamma convolution
• generalised negative-binomial convolution
• unimodality