On the Distributions of Scan Statistics of a Two-Dimensional Poisson Process
- 1 March 1997
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 29 (1) , 1-18
- https://doi.org/10.2307/1427857
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
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