Simulation Master Tutorials > Entering Copulas in a Model > Copula Direction

Simulation Master employs bivariate copulas to model a correlation structure between two random variables. A copula allows for changing correlation depending on the values of the variables. One of the features of copulas is that we need to specify a direction in order to model the correlation properly. Simulation Master uses a number at the end of each copula type to specify direction. For example, the Clayton copula can have four directions as shown below.

When fitting a copula or adding a copula to a model, the direction will depend on how the two variables are correlated. For example, in a Clayton 1 copula the variables are highly correlated when both variables have low values and less so as they increase. On the other hand, in a Clayton 4 copula the variables are highly correlated when both variables have high values and less so as they decrease.

Clayton and Gumbel copulas can have four possible directions. The Frank and FGM copulas are symmetrical, and therefore only require two directions.

The copula tool has example scatter plots of each copula and direction to help visualize the correlation structure. To see this, click the *Copula* button on the ribbon.