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e^||^\frac\Gamma_p(\frac)} * is the multivariate gamma function * is the trace function | cdf = | mean = | median = | mode = for | variance = | skewness = | kurtosis = | entropy =see below | mgf = | char = }} In statistics, the Wishart distribution is a generalization to multiple dimensions of the chi-squared distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution. It is named in honor of John Wishart, who first formulated the distribution in 1928. 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. ==Definition== Suppose is an matrix, each row of which is independently drawn from a with zero mean: : Then the Wishart distribution is the probability distribution of the random matrix known as the scatter matrix. One indicates that has that probability distribution by writing : The positive integer is the number of ''degrees of freedom''. Sometimes this is written . For the matrix is invertible with probability if is invertible. If then this distribution is a chi-squared distribution with degrees of freedom. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Wishart distribution」の詳細全文を読む スポンサード リンク
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