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

DOI10.2307/1427857zbMath0883.60046OpenAlexW2091144713MaRDI QIDQ4339335

Sven Erick Alm

Publication date: 3 July 1997

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1427857

zbMATH Keywords

Poisson fieldrectangular windowmaximum scan statistic

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Approximations to statistical distributions (nonasymptotic) (62E17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Optimal and fast detection of spatial clusters with scan statistics ⋮ Multiple window scan statistics for two dimensional Poisson processes ⋮ Using scan statistics for cluster detection: recognizing real bandwagons ⋮ New approximations for the distribution of the \(r\)-scan statistic ⋮ Geographic and network surveillance via scan statistics for critical area detection ⋮ Importance sampling for spatial scan analysis: computing scan statistic \(p-\)values for marked point processes. ⋮ Maximum scan score-type statistics ⋮ A Wilcoxon-Mann-Whitney spatial scan statistic for functional data ⋮ Spatial point process models of defensive strategies: detecting changes ⋮ A Tree-Based Scan Statistic for Database Disease Surveillance ⋮ Maxima of moving sums in a Poisson random field ⋮ Change-point problems: bibliography and review ⋮ Poisson approximation in connection with clustering of random points ⋮ Variable Window Scan Statistics for Normal Data

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