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Multivariate Student distribution : ウィキペディア英語版
Multivariate t-distribution
|
cdf =No analytic expression|
mean =\boldsymbol\mu if \nu > 1; else undefined|
median =\boldsymbol\mu|
mode =\boldsymbol\mu|
variance =\frac \boldsymbol\Sigma if \nu > 2; else undefined|
skewness =0|
kurtosis =|
entropy =|
mgf =|
char =|
}}
In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random vectors of the Student's t-distribution, which is a distribution applicable to univariate random variables. While the case of a random matrix could be treated within this structure, the matrix t-distribution is distinct and makes particular use of the matrix structure.
==Definition==
One common method of construction of a multivariate t distribution, for the case of p dimensions, is based on the observation that if \mathbf y and u are independent and distributed as (,) and \chi^2_\nu (i.e. multivariate normal and chi-squared distributions) respectively, the covariance \mathbf\, is a ''p'' × ''p'' matrix, and \sqrt=-, then has the density
:
\frac\left|\right|^\left(multivariate Cauchy distribution.

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「Multivariate t-distribution」の詳細全文を読む



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