In statistics, the Wishart distribution, named in honor of John Wishart, is any of a family of probability distributions for nonnegative-definite matrix-valued random variables ("random matrices"), defined as follows. Suppose
Further suppose X1, ..., Xn are independent and identically distributed. Then the Wishart distribution is the probability distribution of the p×p random matrix
If p = 1 and V = 1 then this distribution is a chi-square distribution.
The Wishart distribution arises frequently in likelihood-ratio tests in multivariate statistical analysis.