Multivariate Student Distribution - Definition

Definition

One common method of construction of a multivariate t distribution, for the case of dimensions, is based on the observation that if and are independent and distributed as and (i.e. multivariate normal and chi-squared distributions) respectively, then is a p × p matrix, and, then has the density

\frac{\Gamma\left}{\Gamma(\nu/2)\nu^{p/2}\pi^{p/2}\left|{\boldsymbol\Sigma}\right|^{1/2}\left^{(\nu+p)/2}}

and is said to be distributed as a multivariate t-distribution with parameters .

In the special case, the distribution is a multivariate Cauchy distribution.

Read more about this topic:  Multivariate Student Distribution

Famous quotes containing the word definition:

    “Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?”
    —Richard Eberhart (b. 1904)

    “I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
    —Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    “One definition of man is “an intelligence served by organs.””
    —Ralph Waldo Emerson (1803–1882)