# Random Variable Set (editor)

Random Variable Sets are meant to handle correlation between Random Variables. If not defined all the random variables are considered uncorrelated.

Configuring a Random Variable Set requires to set the following parameters:

## Meta Data

Name and description are as defined in the wizard

## Type

Standard random variable sets and Gaussian mixture random variables sets can be created. In the standard random variable sets, the variables are fully defined with their marginals and correlation. The Gaussian mixture random variables sets consist of several kernel with a (multi-) normal distribution.

### Standard random variable sets

In the case of standard random variable sets, the fields Random Variables and Correlation needs to be specified

#### Random Variables

Selection of the Random Variables to be used. Random Variables are added to a set using , they are removed using . The order of the variables can be changed using and . These buttons are on the left side of the perspective, it might be necessary to resize it or scroll to make them visible. Each set must contain at least one random variable.

#### Correlation

Correlation between the random variables. If unspecified, they are assumed to be uncorrelated. Only the lower part of the matrix has to be defined, COSSAN-X completes it by symmetry. The names of the Random Variables corresponding to each member of the correlation matrix are written above the first row and at the left of the first column of the matrix (in the example shown below, the random variables are named E, f and h).

By default, the unspecified terms of the matrix which are not on its diagonal are set to zero (uncorrelated variables). The correlation matrix must be positive-definite. A random variable set with erroneous correlation matrix can not be saved Very high correlations among Random Variables Some distributions do not allow high correlation coefficient (because of their statistical nature), although the correlation matrix is valid (positive-definite). In such case, an error is raised at the beginning of the analysis

### Gaussian mixture random variable sets

Gaussian mixture random variable are dedicated to modeling any distribution by the means of kernels distributed according to a Gaussian distribution.

Random Variables are added to a set using , they are removed using . The order of the variables can be changed using and . The name of each variable must be specified (and each name is unique). The dimension of the set is equal to the number of random variables.

The correlation between the different variables has to be specified. Only the lower part of the matrix has to be defined, COSSAN-X completes it by symmetry. The names of the Random Variables corresponding to each member of the correlation matrix are written above the headers of the rows and of the columns of the matrix.

The central points of the kernels have to be specified. Double click on one of the coordinate to change its value. The coordinate of the central points are added using , they are removed using .