Question

Write about the wishart matrix - its distribution
and properties​

Answer 1

Answer:

The Wishart distribution can be characterized by its probability density function as follows: Let X be a p × p symmetric matrix of random variables that is positive definite. Let V be a (fixed) symmetric positive definite matrix of size p × p. for other matrices the density is equal to zero.

PDF: Γp is the multivariate gamma function; tr is the trace function

Parameters: n > p − 1 degrees of freedom (real); V > 0 scale matrix (p × p pos. def)

Support: X(p × p) positive definite matrix

Notation: X ~ Wp(V, n)