MultiNormal

[[Category::Multivariate Distributions]]

MultiNormal( m, s, c, i, j )

A multi-variate normal (or Gaussian) distribution with mean m, standard deviation s, and correlation matrix cm. m and s may be scalar or indexed by i. cm must be symmetric, positive-definite, and indexed by i & j, which must be the same length.

Multinormal uses a correlation matrix. Compare with Gaussian, which also defines a multi-variate normal but which uses a covariance matrix.

Library

Multivariate Distribution.ana

Notes

MultiNormal can be used with the Random function to generate a single multivariate sample point, indexed by I. E.g.:

Random( MultiNormal(m,s,c,i,j) )

To generate independent samples along one or more indexes K1,K2,K3, use the Over parameter, e.g.:

MultiNormal(m,s,c,i,j,Over:K1,K2,K3)

See Gaussian for an example.

See Also

• Gaussian : Multivariate normal specified using covariance rather than correlation.
• Normal : 1-D normal distribution
• BiNormal, Normal_correl : 2-D normal distributions
• Random
• Correlation : For estimating a sample correlation matrix from data.