# Inverse-Wishart distribution

Probability distribution / From Wikipedia, the free encyclopedia

In statistics, the **inverse Wishart distribution**, also called the **inverted Wishart distribution**, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a
multivariate normal distribution.

**Quick facts: Notation, Parameters, Support, PDF, Mean...**▼

Notation | |||
---|---|---|---|

Parameters |
degrees of freedom (real) , scale matrix (pos. def.) | ||

Support |
is p × p positive definite | ||

- is the multivariate gamma function
- is the trace function
| |||

Mean | For | ||

Mode |
[1]^{: 406 } | ||

Variance | see below |

We say follows an inverse Wishart distribution, denoted as , if its inverse has a Wishart distribution . Important identities have been derived for the inverse-Wishart distribution.[2]