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

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