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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: p0 = e–m; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n2) 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
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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