## You are here

HomeWishart distribution

## Primary tabs

# Wishart distribution

Let $U_{i}\sim N_{p}(\mu_{i},\Sigma),\quad i=1,\ldots,k$ be independent $p$-dimensional random variables, which are
multivariate normally distributed.
Let $S=\sum_{{i=1}}^{k}U_{i}{U_{i}}^{T}$. Let $M$ be the $k\times p$ matrix
with $\mu_{1},\ldots,\mu_{k}$ as rows.
Then the joint distribution of the
elements of $S$ is said to be a *Wishart distribution on* $k$
*degrees of freedom *, and is
denoted by $W_{p}(k,\Sigma,M)$. If $M=0$, the distribution is said to be
*central* and is denoted by $W_{p}(k,\Sigma)$.
The Wishart distribution is a multivariate generalization of the $\chi^{2}$ distribution.

$W_{p}$ has a density function when $k\geq p$.

Defines:

central Wishart distribution

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

62H05*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections