Multivariate t | t distribution and gamma distribution
Instatistics,themultivariatet-distribution(ormultivariateStudentdistribution)isamultivariateprobabilitydistribution.ItisageneralizationtorandomvectorsoftheStudentst-distribution,whichisadistributionapplicabletounivariaterandomvariables.Whilethecaseofarandommatrixcouldbetreatedwithinthisstructure,thematrixt-distributionisdistinctandmakesparticularuseofthematrixstructure.Definition[edit]Onecommonmethodofconstructionofamultivariatet-distribution,forthecaseofp{displaystylep}dimensions,isbasedont...
In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random vectors of the Students 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[edit]One common method of construction of a multivariate t-distribution, for the case of p{displaystyle p} dimensions, is based on the observation that if y{displaystyle mathbf {y} } and u{displaystyle u} are independent and distributed as N(0,Σ){displaystyle {mathcal {N}}({mathbf {0} },{oldsymbol {Sigma }})} and χν2{displaystyle chi _{ u }{2}} (i.e. multivariate normal and chi-squared distributions) respectively, the matrix Σ{displaystyle mathbf {Sigma } ,} is a p × p matrix, and y/u/ν=x−μ{displaystyle {mathbf {y} }/{...