# MultiNormal

## Contents

## 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» and «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 Distributions library functions (Multivariate Distributions.ana)

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## Example

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

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

`Variable M :=`

I ▶ 1 2 3 4 10 -5 0 7

`Variable S :=`

I ▶ 1 4 16 9 10 -5 0 7

`Variable Cor :=`

I ▶ J ▼ 1 2 3 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

`MultiNormal(M, S, C, I, J) →`

(The above graphs are scatter plots in sample view, using `I`

as the coordinate index.)

### Single Random Sample

MultiNormal may be used with the Random function to generate a single random vector, indexed by `I`

, drawn from the multi-variate Gaussian distribution. Using the above variables, the usage is:

`Random(MultiNormal(M, CV, I, J))`

### Independent samples

The «Over» parameter can also be used with **MultiNormal** to generate multivariate samples that are independent over additional indexes. For example, to generate an independent **MultiNormal** for each element of Index `K`

, use:

`MultiNormal(M, CV, I, J, Over: K)`

## 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.
- Multivariate distributions
- Multivariate Distributions.ana

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