On the existence of non-central Wishart distributions

Details On the existence of non-central Wishart distributions On the existence of non-central Wishart distributions

2010-09-02

arxiv.org/abs/1009.0473v4

Mathematics

Probability

Following Gerard Letac's suggestion, I upload a new version with self-contained proofs of the statements in section 3. I use m

Scientific paper

This paper deals with the existence issue of non-central Wishart distributions which is a research topic initiated by Wishart (1928), and with important contributions by e.g., L\'evy (1937), Gindikin (1975), Shanbhag (1988), Peddada and Richards (1991). We present a new method involving the theory of affine Markov processes, which reveals joint necessary conditions on shape and non-centrality parameter. While Eaton's conjecture concerning the necessary range of the shape parameter is confirmed, we also observe that it is not sufficient anymore that it only belongs to the Gindikin ensemble, as is in the central case.

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