Analysis of the Luria–Delbrück distribution using discrete convolution powers
- 1 June 1992
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 29 (2) , 255-267
- https://doi.org/10.2307/3214564
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;wheremis the expected number of mutations. A new relation for the asymptotic behavior ofpn(≈c/n2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for thez-transform of the distribution is also reported.Keywords
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