On the existence of non-central Wishart distributions
Abstract
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.
Keywords
Cite
@article{arxiv.1009.0473,
title = {On the existence of non-central Wishart distributions},
author = {Eberhard Mayerhofer},
journal= {arXiv preprint arXiv:1009.0473},
year = {2021}
}
Comments
This version contains an Appendix which explains the relation of my definition of non-central Wishart distributions to alternative ones from the standard literature