Wishart Distribution - The Possible Range of The Shape Parameter

The Possible Range of The Shape Parameter

It can be shown that the Wishart distribution can be defined if and only if the shape parameter n belongs to the set

\Lambda_p:=\{0,\dots,p-1\}\cup \left(p-1,\infty\right).

This set is named after Gindikin, who introduced it in the seventies in the context of gamma distributions on homogeneous cones. However, for the new parameters in the discrete spectrum of the Gindikin ensemble, namely,

\Lambda_p^*:=\{0,\dots,p-1\},

the corresponding Wishart distribution has no Lebesgue density.

Read more about this topic:  Wishart Distribution

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