Ratios of ordered points of point processes with regularly varying intensity measures
Ipsen, Yuguang; Maller, Ross; Resnick, Sidney I.
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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