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Analysis of the Luria-Delbrück Distribution Using Discrete Convolution Powers

W. T. Ma, G. Vh. Sandri and S. Sarkar
Journal of Applied Probability
Vol. 29, No. 2 (Jun., 1992), pp. 255-267
DOI: 10.2307/3214564
Stable URL: http://www.jstor.org/stable/3214564
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Analysis of the Luria-Delbrück Distribution Using Discrete Convolution Powers
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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; pn = (m/n) Σi = 0 n - 1 pi/(n - i + 1) 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.

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