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## A Raikov-Type Theorem for Radial Poisson Distributions: A Proof of Kingman's Conjecture

### Abstract

In the present paper we prove the following conjecture in Kingman, J.F.C., Random walks with spherical symmetry, Acta Math.,109, (1963), 11-53. concerning a famous Raikov's theorem of decomposition of Poisson random variables: "If a radial sum of two independent random variables X and Y is radial Poisson, then each of them must be radial Poisson."Comment: 6 pgs. The paper presents a proof of a Kingman conjecture regarding an analogue of the Raikov's Theorem for Kingman convolution

Topics: Mathematics - Statistics Theory
Year: 2011
OAI identifier: oai:arXiv.org:1103.5243