Wishart Distribution - Definition

Definition

Suppose X is an n × p matrix, each row of which is independently drawn from a p-variate normal distribution with zero mean:

Then the Wishart distribution is the probability distribution of the p×p random matrix

known as the scatter matrix. One indicates that S has that probability distribution by writing

The positive integer n is the number of degrees of freedom. Sometimes this is written W(V, p, n). For np the matrix S is invertible with probability 1 if V is invertible.

If p = 1 and V = 1 then this distribution is a chi-squared distribution with n degrees of freedom.

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