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Analysis of the Luria–Delbrück distribution using discrete convolution powers

Part of:Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

W. T. Ma,
G. vH. Sandri and
S. Sarkar
W. T. Ma
Affiliation:
Boston University
G. vH. Sandri
Affiliation:
Boston University
S. Sarkar*
Affiliation:
Boston University
*
∗ Postal address: Boston Theoretical Biology Group, Center for the Philosophy and History of Science, Boston University, 745 Commonwealth Avenue, Boston, MA 02215, USA.
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Abstract

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p 0 = e–m ; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n 2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.

Keywords

BACTERIAL MUTAGENESISDIRECTED MUTATIONS

MSC classification

Primary:60E05: Distributions
Secondary:92D10: Genetics

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992, pp. 255 - 267
Copyright
Copyright © Applied Probability Trust 1992 

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