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

Famous quotes containing the words range and/or shape:

    “Whereas children can learn from their interactions with their parents how to get along in one sort of social hierarchy—that of the family—it is from their interactions with peers that they can best learn how to survive among equals in a wide range of social situations.”
    —Zick Rubin (20th century)

    “But virtue, as it never will be moved,
    Though lewdness court it in a shape of heaven,
    So lust, though to a radiant angel linked,
    Will sate itself in a celestial bed
    And prey on garbage.”
    —William Shakespeare (1564–1616)