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Analysis of the Luria–Delbrück distribution using discrete convolution powers

Published online by Cambridge University Press:  14 July 2016

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.

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.

MSC classification

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1992 

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