Wishart distribution

Introduction

In statistics, the Wishart distribution is generalization to multiple dimensions of the chi-squared distribution (卡方分布), or, in the case of non-integer degrees of freedom, of the gamma distribution.

It is a family of probability distributions defined over symmetric, nonnegative-definite matrix-valued random variables (“random matrices”). These distributions are of great importance in the estimation of covariance matrices in multivariate statistics. In Bayesian statistics, the Wishart distribution is the conjugate prior of the inverse covariance-matrix of a multivariate-normal random-vector.