The errors are usually assumed to follow a multivariate normal distribution.

Rectangular confidence regions for the means of multivariate normal distributions.

Moreover, every finite collection of those random variables has a multivariate normal distribution.

This early work assumed that data-values within each of the two groups had a multivariate normal distribution.

The multivariate normal distribution is the special case in which for quadratic form .

It is constructed from a multivariate normal distribution over by using the probability integral transform.

Under the unimodality hypothesis, the data are thought to be a random sample from a multivariate normal distribution.

The texture in each region is modeled by a multivariate normal distribution whose entropy has closed form expression.

The results for the special case of the Multivariate normal distribution is originally attributed to Maxwell.

Statistically, the prior probability distribution of is sometimes taken to be a multivariate normal distribution.

The matrix normal is related to the multivariate normal distribution in the following way:

However, if does follow a multivariate normal distribution, the variance of the quadratic form becomes particularly tractable.

Then, the multivariate normal distribution can be equivalently represented as a moment matrix:

The proof for this follows from the definitions of multivariate normal distributions and linear algebra.

For general multivariate normal distributions for and the data error, one can apply a transformation of the variables to reduce to the case above.

The continuous analogue is Multivariate normal distribution.

More specifically, the distribution can be defined in terms of a quadratic form derived from a multivariate normal distribution.

Monte Carlo simulation generates random market scenarios drawn from that multivariate normal distribution.

The z must be sampled from a truncated multivariate normal distribution to preserve their rank ordering.

Also see multivariate normal distribution.

The multivariate stable distribution can also be thought as an extension of the multivariate normal distribution.

The multivariate normal distribution is a commonly encountered multivariate distribution.

The multivariate normal distribution describes the Gaussian law in the k-dimensional Euclidean space.

The normal distribution and multivariate normal distributions.

The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is a multivariate normal distribution.