Progress of a half century in the study of the Luria-Delbruck distribution

被引：104

作者：

Zheng, Q ^{[1
]}

机构：

[1] Natl Ctr Toxicol Res, Div Biometry & Risk Assessment, Jefferson, AR 72079 USA

来源：

MATHEMATICAL BIOSCIENCES | 1999年 / 162卷 / 1-2期

关键词：

Luria-Delbruck model; Luria-Delbruck distribution; estimation of mutation rate; Poisson-stopped-sum distribution; filtered Poisson process;

D O I：

10.1016/S0025-5564(99)00045-0

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The Luria-Delbruck mutation model has been mathematically formulated in a number of ways. This review article examines four most important formulations, focusing on important practical issues closely linked with the distribution of the number of mutants. These issues include the probability generating functions, moments (cumulants), computational methods and asymptotics. This review emphasizes basic principles which not only help to unify existing results but also allow for a few useful extensions. In addition, the review offers a historical perspective and some new explanations of divergent moments. (C) 1999 Published by Elsevier Science Inc. All rights reserved.

引用

页码：1 / 32

页数：32

共 36 条

[1]

[Anonymous], 1955, An introduction to stochastic processes, with special reference to methods and applications

[2] STATISTICAL CONCEPTS IN THE THEORY OF BACTERIAL MUTATION [J].

ARMITAGE, P .

JOURNAL OF HYGIENE, 1953, 51 (02) :162-184

[3]

ARMITAGE P, 1952, J ROY STAT SOC B, V14, P1

[4]

Bailey N. T. J., 1964, ELEMENTS STOCHASTIC

[5]

Bartlett MS., 1978, INTRO STOCHASTIC PRO

[6] THE ORIGIN OF MUTANTS [J].

CAIRNS, J ;

OVERBAUGH, J ;

MILLER, S .

NATURE, 1988, 335 (6186) :142-145

[7]

Chung KL., 1974, COURSE PROBABILITY T

[8]

CRUMP KS, 1974, BIOMETRIKA, V61, P237, DOI 10.1093/biomet/61.2.237

[9] ASYMPTOTICS OF THE LURIA-DELBRUCK DISTRIBUTION [J].

GOLDIE, CM .

JOURNAL OF APPLIED PROBABILITY, 1995, 32 (03) :840-841

[10]

Johnson N.L., 1992, UNIVARIATE DISCRETE

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