Wishart Distribution - Relationships To Other Distributions

Relationships To Other Distributions

• The Wishart distribution is related to the Inverse-Wishart distribution, denoted by, as follows: If and if we do the change of variables, then . This relationship may be derived by noting that the absolute value of the Jacobian determinant of this change of variables is, see for example equation (15.15) in.
• In Bayesian statistics, the Wishart distribution is a conjugate prior for the precision parameter of the multivariate normal distribution, when the mean parameter is known.
• A generalization is the multivariate gamma distribution.
• A different type of generalization is the normal-Wishart distribution, essentially the product of a multivariate normal distribution with a Wishart distribution.