Ratios of Ordered Points of Point Processes with Regularly Varying Intensity Measures
Probability
2017-08-01 v1
Abstract
We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to "large-trimming" properties of extremal processes and a variety of applications. Our point process approach facilitates a connection with the negative binomial process of Gregoire (1984) and consequently to certain generalised versions of the Poisson-Dirichlet distribution.
Keywords
Cite
@article{arxiv.1707.09653,
title = {Ratios of Ordered Points of Point Processes with Regularly Varying Intensity Measures},
author = {Yuguang Ipsen and Ross Maller and Sidney Resnick},
journal= {arXiv preprint arXiv:1707.09653},
year = {2017}
}