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Analysis of the Luria–Delbrück distribution using discrete convolution powers

  • W. T. Ma (a1), G. vH. Sandri (a1) and S. Sarkar (a1)


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: p 0 = 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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Postal address: Boston Theoretical Biology Group, Center for the Philosophy and History of Science, Boston University, 745 Commonwealth Avenue, Boston, MA 02215, USA.


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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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