Gaussian distribution

Gaussian(meanVec : numeric[I],covar : numeric[I,J]; I,J:IndexType)

A multi-variate Gaussian distribution based on a mean vector and covariance matrix. The covariance matrix must symmetric and positive-definite. The meanVec is indexed by I. The covariance matrix is 2-D, indexed by I & J. Indexes I & J should be the same length.

Library

Multivariate Distributions.ana

Example

Index I := [1,2,3,4]
Index J := [1,2,3,4]

Variable M := Table(I)

I →	1	2	3	4
	10	-5	0	7

Variable CV := Table(I,J)

		I
		1	2	3	4
J	1	1	-0.5	0.3	0.7
	2	-0.5	1	-0.8	-0.2
	3	0.3	-0.8	1	0.4
	4	0.7	-0.2	0.4	1

Gaussian( M, CV, I, J ) →

[image:Gaussian1_2.jpg] [image:Gaussian1_4.jpg] [image:Gaussian2_4.jpg]

(The above graphs are scatter plots in sample view, using I as the coordinate index.)

See Also

• Normal : for 1-D normal
• BiNormal, Normal_correl : For 2-D normals
• MultiNormal : For multi-D normal (Gaussian) using correlation, rather than covariance
• Variance (see: use of Variance for estimating sample covariance from data)