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An improved Poisson limit theorem for sums of dissociated random variables

Published online by Cambridge University Press:  14 July 2016

A. D. Barbour  and
G. K. Eagleson
A. D. Barbour*
Affiliation:
Universität Zürich
G. K. Eagleson*
Affiliation:
CSIRO Division of Mathematics and Statistics
*
∗Postal address: Institut für Angewandte Mathematik, Universität Zürich, CH-8001, Zürich, Switzerland.
∗∗Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield, NSW 2070, Australia.
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Abstract

A Poisson limit theorem for sums of dissociated 0–1 random variables is refined by deriving the first terms in an asymptotic expansion. The most natural refinement does not remove all the first-order error in a number of applications to tests of clustering, and a further approximation is derived which gives excellent results in practice. The proofs are based on the technique of Stein and Chen.

Keywords

CORRELATIONSINTERPOINT DISTANCESPOISSON APPROXIMATIONSRATES OF CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 586 - 599
Copyright
Copyright © Applied Probability Trust 1987 

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References

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