论文信息 - Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions

Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions

Given a Poisson process in two or three dimensions, we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area. The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions. The accuracy of the approximation is checked through simulation.

Sven Erick Alm

[1] M. Bartlett,et al. The expected number of aggregates in a random distribution of n points , 1950, Mathematical Proceedings of the Cambridge Philosophical Society.

[2] Joseph Naus,et al. Approximations for Distributions of Scan Statistics , 1982 .

[3] S. Janson. Bounds on the distributions of extremal values of a scanning process , 1984 .

[4] D. Aldous. Probability Approximations via the Poisson Clumping Heuristic , 1988 .

[5] Some limit theorems for the homogeneous Poisson process , 1991 .

[6] C. Loader. Large-deviation approximations to the distribution of scan statistics , 1991, Advances in Applied Probability.

[7] M Kulldorff,et al. Spatial disease clusters: detection and inference. , 1995, Statistics in medicine.

[8] M. Kulldorff,et al. Childhood leukaemia in Sweden: using GIS and a spatial scan statistic for cluster detection. , 1996, Statistics in medicine.

[9] Sven Erick Alm. On the Distributions of Scan Statistics of a Two-Dimensional Poisson Process , 1997, Advances in Applied Probability.