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

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

2011-03-27

arxiv.org/abs/1103.5243v3

Mathematics

Statistics Theory

6 pgs. The paper presents a proof of a Kingman conjecture regarding an analogue of the Raikov's Theorem for Kingman convolutio

Scientific paper

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."

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