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Throwing stones and collecting bones: Looking for Poisson‐like random measures
Author(s) -
Bastian Caleb Deen,
Rempala Grzegorz A.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6224
Subject(s) - mathematics , poisson distribution , binomial (polynomial) , subspace topology , simple random sample , negative binomial distribution , class (philosophy) , simple (philosophy) , statistics , mathematical analysis , artificial intelligence , computer science , population , philosophy , epistemology , demography , sociology
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.