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A new discrete distribution induced by the Luria-Delbruck mutation model
by
Qi Zheng
Texas A&M School of Rural Public Health, College Station, Texas 77843
The Luria-Delbruck mutation model has been a subject of mathematical investigation for over six decades. A recent investigation of this celebrated model led to the discovery of a new discrete distribution that can potentially be applied to model data generated by other biological processes. This two-parameter distribution arises as a limiting form of the probability generating function discovered by M.S. Bartlett. We first show that an obvious extension of the limiting form is a valid probability generating function and then present an algorithm for computing the probability mass function. The asymptotic behavior of the probability mass function is revealed by employing the technique of singularity analysis of generating functions. We also suggest likelihood based algorithms for estimating the parameters. The new distribution is found to be infinitely divisible and possess divergent moments.
Date received: April 29, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawd-41.