Ratios of ordered points of point processes with regularly varying intensity measures |
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| Authors: | Yuguang Ipsen Ross Maller Sidney Resnick |
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| Affiliation: | 1. Research School of Finance, Actuarial Studies and Statistics, Australian National University, Australia;2. School of Operations Research and Information Engineering, Cornell University, United States |
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| 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. |
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| Keywords: | Regular variation Poisson points Lévy process Negative binomial Trimming Order statistics |
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