Computing the distribution of the maximum in balls-and-boxes problems, with application to clusters of disease cases

Details Computing the distribution of the maximum in balls-and-boxes problems, with application to clusters of disease cases Computing the distribution of the maximum in balls-and-boxes problems, with application to clusters of disease cases

2006-10-26

arxiv.org/abs/math/0610810v1

Mathematics

Statistics Theory

Scientific paper

10.1073/pnas.0704691104

We present a rapid method for the exact calculation of the cumulative distribution function of the maximum of multinomially distributed random variables. The method runs in time $O(mn)$, where $m$ is the desired maximum and $n$ is the number of variables. We apply the method to the analysis of two situations where an apparent clustering of cases of a disease in some locality has raised the possibility that the disease might be communicable, and this possibility has been discussed in the recent literature. We conclude that one of these clusters may be explained on purely random grounds, whereas the other may not.

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