Wishart distribution

Let UiNp(μi,Σ),i=1,,k be independent p-dimensional random variablesMathworldPlanetmath, which are multivariate normally distributed (http://planetmath.org/jointnormaldistribution). Let S=i=1kUiUiT. Let M be the k×p matrix with μ1,,μk as rows. Then the joint distributionPlanetmathPlanetmath of the elements of S is said to be a Wishart distributionMathworldPlanetmath on k of freedom , and is denoted by Wp(k,Σ,M). If M=0, the distributionPlanetmathPlanetmath is said to be central and is denoted by Wp(k,Σ). The Wishart distribution is a multivariate generalizationPlanetmathPlanetmath of the χ2 distribution.

Wp has a density function when kp.

Title Wishart distribution
Canonical name WishartDistribution
Date of creation 2013-03-22 16:12:31
Last modified on 2013-03-22 16:12:31
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 9
Author Mathprof (13753)
Entry type Definition
Classification msc 62H05
Defines central Wishart distribution