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Throwing stones and collecting bones: Looking for Poisson-like random measures |
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| Authors: | Caleb Deen Bastian Grzegorz A Rempala |
| Institution: | 1. Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey;2. Division of Biostatistics and Department of Mathematics, The Ohio State University, Columbus, Ohio |
| Abstract: | We show that in a broad class of random counting measures, one may identify only three that are rescaled versions of themselves when restricted to a subspace. These are Poisson, binomial, and negative binomial random measures. We provide some simple examples of possible applications of such measures. |
| Keywords: | Laplace functional Poisson-type (PT) distributions random counting measure stone throwing construction strong invariance thinning |