Cited by 146Stochastic processes and statistical mechanicsEvolution and Genetic DynamicsProbability and Statistical Research

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Analysis of the Luria–Delbrück distribution using discrete convolution powers

Ma, W. T., Sandri, G. vH., Sarkar, S.·1992·Journal of Applied Probability

DOI 10.1017/s0021900200043023

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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/n^2) 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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Authors: Ma, W. T., Sandri, G. V., & Sarkar, S.
Affiliations: Boston University (US)
Corresponding author: Sarkar, S.
ORCID: Sarkar, S.
Venue: Journal of Applied Probability
Publisher: Cambridge University Press (CUP)
Published: 1992-06
Volume: 29
Issue: 2
Pages: 255-267
ISSN: 0021-9002 (ISSN-L)
1475-6072
DOI: 10.1017/s0021900200043023
OpenAlex: W2320526527
Cited by: 146
References: 10
Citations by year: 2026: 4 · 2025: 1 · 2024: 1 · 2023: 9 · 2022: 4 · 2021: 7 · 2020: 2 · 2019: 5 · 2018: 4 · 2017: 9 · 2016: 5 · 2015: 11 · 2014: 8 · 2013: 4 · 2012: 8
FWCI: 5.46
Type: journal article
Language: en
Open access: closed
Licence: www.cambridge.org/core/terms (unspecified, 8809 d)
Locations: Journal of Applied Probability (publishedVersion)
Topics: Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Keywords: recurrence relations, population genetics, asymptotic behavior, z-transform

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Analysis of the Luria–Delbrück distribution using discrete convolution powers

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