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...

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...

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

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

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...

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

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

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...

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

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...

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...

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

covariance matrix Γ {\displaystyle \Gamma } , and the relation matrix C {\displaystyle C} . The standard complex normal is the univariate distribution with...

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

Leslie matrix is a discrete, age-structured model of population growth named after Patrick H. Leslie and used in population ecology. The Leslie matrix (also...

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....

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

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...

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

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...

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

prior of a multivariate normal distribution with an unknown mean and covariance matrix (the inverse of the precision matrix). Suppose μ | μ 0 , λ , Σ ∼ N...

prior of a multivariate normal distribution with unknown mean and precision matrix (the inverse of the covariance matrix). Suppose μ | μ 0 , λ , Λ ∼ N...

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

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