In statistics, the matrix normal distribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariate...

In statistics, the matrix t-distribution (or matrix variate t-distribution) is the generalization of the multivariate t-distribution from vectors to matrices...

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...

{\boldsymbol {\Sigma }}} . inverse matrix gamma distribution. matrix normal distribution. matrix t-distribution. Wishart distribution. Iranmanesh, Anis, M. Arashib...

. inverse Wishart distribution. matrix gamma distribution. matrix normal distribution. matrix t-distribution. Wishart distribution. Iranmanesha, Anis;...

In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform. They were...

statistics, Student's t distribution (or simply the t distribution) t ν {\displaystyle t_{\nu }} is a continuous probability distribution that generalizes...

p\times p} random matrix with a Wishart distribution W ( I p , p , m ) {\displaystyle W(\mathbf {I} _{p,p},m)} with unit scale matrix and m degrees of...

In statistics, the matrix F distribution (or matrix variate F distribution) is a matrix variate generalization of the F distribution which is defined on...

first formulated the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually...

increased. The matrix von Mises-Fisher distribution (also known as matrix Langevin distribution) has the density f n , p ( X ; F ) ∝ exp ⁡ ( tr ⁡ ( F T X ) ) {\displaystyle...

distribution The matrix t-distribution The Matrix Langevin distribution The matrix variate beta distribution The Uniform distribution on a Stiefel manifold...

In statistics, the matrix variate beta distribution is a generalization of the beta distribution. If U {\displaystyle U} is a p × p {\displaystyle p\times...

k\times \ell } matrix A {\displaystyle {\boldsymbol {A}}} such that A Z {\displaystyle {\boldsymbol {A}}\mathbf {Z} } has the same distribution as X {\displaystyle...

It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov...

In mathematics, the spectrum of a matrix is the set of its eigenvalues. More generally, if T : V → V {\displaystyle T\colon V\to V} is a linear operator...

matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution....

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is Q T Q = Q Q T = I...

F_{a}(x)=\left\{{\begin{matrix}1,&{\mbox{if }}x\geq a\\0,&{\mbox{if }}x<a\end{matrix}}\right.} Such degenerate distributions often arise as limits of...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

multivariate normal distribution and for matrices in the matrix normal distribution. The simplest case of a normal distribution is known as the standard...

matrix of the Gaussian distribution that underlies the Bingham distribution. Directional statistics von Mises–Fisher distribution Kent distribution Bingham...

In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column...

of the log-t distribution exist. In this case, the location parameter is replaced by a vector μ, the scale parameter is replaced by a matrix Σ. Olosunde...

correlation coefficient Matrix gamma distribution Matrix normal distribution Matrix population models Matrix t-distribution Mauchly's sphericity test...

function of this distribution is f ( k ) = { 1 / 2 if  k = − 1 , 1 / 2 if  k = + 1 , 0 otherwise. {\displaystyle f(k)=\left\{{\begin{matrix}1/2&{\text{if...

definite matrix which is proportional to the covariance matrix if the latter exists. Examples include the following multivariate probability distributions: Multivariate...

beta distribution is a five-parameter distribution family which has the beta distribution as a special case. The matrix variate beta distribution is a...

the covariance matrix of a multivariate normal distribution. We say X {\displaystyle \mathbf {X} } follows an inverse Wishart distribution, denoted as X...