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

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

normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution...

matrices. The matrix t-distribution shares the same relationship with the multivariate t-distribution that the matrix normal distribution shares with the...

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally...

continuous probability distributions. It is the conjugate prior of a multivariate normal distribution with an unknown mean and covariance matrix (the inverse of...

standard normal random variables. The chi-squared distribution χ k 2 {\displaystyle \chi _{k}^{2}} is a special case of the gamma distribution and the...

Bernoulli distribution. The Wishart distribution The inverse-Wishart distribution The Lewandowski-Kurowicka-Joe distribution The matrix normal distribution The...

Wishart distribution is the conjugate prior of the inverse covariance-matrix of a multivariate-normal random vector. Suppose G is a p × n matrix, each column...

normal. The complex normal family has three parameters: location parameter μ, covariance matrix Γ {\displaystyle \Gamma } , and the relation matrix C...

Wishart distribution, and is used similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution...

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

covariance matrix or precision matrix of multivariate normal distributions, and related distributions. The probability density function of the matrix F {\displaystyle...

the half-normal distribution is a special case of the folded normal distribution. Let X {\displaystyle X} follow an ordinary normal distribution, N ( 0...

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

the projected normal distribution (also known as offset normal distribution, angular normal distribution or angular Gaussian distribution) is a probability...

elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. In the simplified...

The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable X with mean...

are random numbers, subject to suitable probability distributions, such as matrix normal distribution. Beyond probability theory, they are applied in domains...

logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If Y is a random variable with a normal...

Wishart distribution, and is used similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution...

In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable...

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

probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate...

continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However...

the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio...

multivariate normal and chi-squared distributions) respectively, the matrix Σ {\displaystyle \mathbf {\Sigma } \,} is a p × p matrix, and μ {\displaystyle...

variables. This is not to be confused with the sum of normal distributions which forms a mixture distribution. Let X and Y be independent random variables that...

{\boldsymbol {\Sigma }}} is the covariance matrix. Unlike the multivariate normal distribution, even if the covariance matrix has zero covariance and correlation...

construction can be generalized by starting with a normal distribution with a general covariance matrix, in which case restricting to ‖ x ‖ = 1 {\displaystyle...