Wishart Distribution
W ~ Wishart_p(n, Σ)
Random-Matrix / Conjugate-Prior Family • Published July 22, 2026
The first random-matrix sheet on the site: John Wishart's 1928 sampling distribution for an estimated covariance matrix, built directly as a sum of outer products of already-published Multivariate Normal draws, with an exact p=1 collapse onto the already-published Chi-Square confirmed numerically. A rare closed-form maximum-likelihood estimator for the scale matrix, and simulation via both the defining construction and the more efficient Bartlett decomposition.
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About This Reference Sheet
The first random-matrix sheet on the site: John Wishart's 1928 sampling distribution for an estimated covariance matrix, built directly as a sum of outer products of already-published Multivariate Normal draws, with an exact p=1 collapse onto the already-published Chi-Square confirmed numerically. A rare closed-form maximum-likelihood estimator for the scale matrix, and simulation via both the defining construction and the more efficient Bartlett decomposition.
Support
W a p×p symmetric positive-definite matrix
Parameters
n ≥ p degrees of freedom, Σ a p×p positive-definite scale matrix