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On the Distributions of Scan Statistics of a Two-Dimensional Poisson Process

Part of: Distribution theory Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Sven Erick Alm
Sven Erick Alm*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden.
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Abstract

Given a two-dimensional Poisson process, X, with intensity λ, we are interested in the largest number of points, L, contained in a translate of a fixed scanning set, C, restricted to lie inside a rectangular area.

The distribution of L is accurately approximated for rectangular scanning sets, using a technique that can be extended to higher dimensions. Reasonable approximations for non-rectangular scanning sets are also obtained using a simple correction of the rectangular result.

Keywords

POISSON PROCESSSCAN STATISTICAPPROXIMATION

MSC classification

Primary: 60G55: Point processes 60G70: Extreme value theory; extremal processes
Secondary: 62E17: Approximations to distributions (nonasymptotic)
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 29 , Issue 1 , March 1997 , pp. 1 - 18
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Research supported by the Axel and Margaret Ax:son Johnson Foundation.

References

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