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We study limiting properties of ratios of ordered points of point processeswhose intensity measures have regularly varying tails, giving a systematictreatment which points the way to "large-trimming" properties of extremalprocesses and a variety of applications. Our point process approach facilitatesa connection with the negative binomial process of Gregoire (1984) andconsequently to certain generalised versions of the Poisson-Dirichletdistribution.

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