Poisson approximation in connection with clustering of random points

• 成果类型: Article
• 署名作者: Månsson, M
• 署名单位: Chalmers University of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 465-492
• 关键词: scan statistics; trials

摘要

Let n particles be independently and uniformly distributed in a rectangle A subset of R-2. Each subset consisting of k less than or equal to n particles may possibly aggregate in such a way that it is covered by some translate of a given convex set C subset of k The number of h-subsets which actually are covered by translates of C is denoted by W. The positions of such subsets constitute a point process on k Each point of this process can be marked with the smallest necessary size of a set, of the same shape and orientation as C, which covers the particles determining the point. This results in a marked paint process. The purpose of this paper is to consider Poisson (process) approximations of W and of the above point processes, by means of Stein's method. To this end, the exact probability for It specific particles to be covered by some translate of C is given.