Analysis of the Luria-Delbrück distribution using discrete convolution powers

Analysis of the Luria-Delbrück distribution using discrete convolution powers

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Article ID: iaor19932402
Country: Israel
Volume: 29
Issue: 2
Start Page Number: 255
End Page Number: 267
Publication Date: Jun 1992
Journal: Journal of Applied Probability
Authors: , ,
Keywords: biology
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: equ1; equ2 where m is the expected number of mutations. A new relation for the asymptotic behavior of equ3 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.

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