Ratios of Ordered Points of Point Processes with Regularly Varying\n Intensity Measures

2017/07/30 by Yuguang Ipsen, Ross Maller, Ipsen, Yuguang +3
Computer Science · Mathematics · #60F05 #60G55 #60G57 #60G70 #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1707.09653

openalex publication_date 2017/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study limiting properties of ratios of ordered points of point processes\nwhose intensity measures have regularly varying tails, giving a systematic\ntreatment which points the way to "large-trimming" properties of extremal\nprocesses and a variety of applications. Our point process approach facilitates\na connection with the negative binomial process of Gregoire (1984) and\nconsequently to certain generalised versions of the Poisson-Dirichlet\ndistribution.\n

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