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
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,
the corresponding Wishart distribution has no Lebesgue density.
Read more about this topic: Wishart Distribution
Famous quotes containing the words range and/or shape:
“The Canadians of those days, at least, possessed a roving spirit of adventure which carried them further, in exposure to hardship and danger, than ever the New England colonist went, and led them, though not to clear and colonize the wilderness, yet to range over it as coureurs de bois, or runners of the woods, or, as Hontan prefers to call them, coureurs de risques, runners of risks; to say nothing of their enterprising priesthood.”
—Henry David Thoreau (1817–1862)
“There are men from whom nature or some peculiar destiny has removed the cover beneath which we hide our own madness. They are like thin-skinned insects whose visible play of muscles seem to make them deformed, though in fact, everything soon turns to its normal shape again.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)