The Wishart

distribution. The Wishart distribution is a useful distribution of random

matrices of sums of squares and cross products. It can be thought of as a

multivariate generalization of the chi-squared distribution. There are various

ways of defining the Wishart distribution, each resulting in the same

distribution. A natural way to define it is in terms of transformations of a

multivariate normal distribution. Let

In the

general case, we

»

The Wishart

distribution. The Wishart distribution is a useful distribution of random

matrices of sums of squares and cross products. It can be thought of as a

multivariate generalization of the chi-squared distribution. There are various

ways of defining the Wishart distribution, each resulting in the same

distribution. A natural way to define it is in terms of transformations of a

multivariate normal distribution. Let

In the

general case, we denote the distribution as

The

importance of the Wishart distribution is that the Wishart matrix

can be

used to make inferences on the variance-covariance matrix _ of

an

underlying multivariate normal distribution.

a) Show

that the probability density function for the (central) Wishart

distribution

is proportional to

»

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