VoseCopulaBiGumbel | Vose Software

# VoseCopulaBiGumbel

{=VoseCopulaBiGumbel(Theta, direction)}

Example model

Array function that returns random values from a bivariate Gumbel copula.

• Theta - Correlation parameter. Can range from -35 (maximum negative correlation) over 0 (no correlation) to 35 (maximum positive correlation)

• Direction - optional parameter that sets the direction of the parameter: can take values 1 (default), 2, 3 or 4.

The output is an array of two cells, with randomly generated copula values between [0,1]. Link the U-parameter of distribution functions to these to generate values of these distributions correlated by this copula.

The optional direction parameter changes the direction of the copula. This can take values 1,2,3,4 according to the number of counterclockwise 90° rotations. Direction 1 (default) means no rotation, 2 means rotated over 90°, 3 means rotated over 180°, and 4 means rotated over 270°.

For the multivariate version of this copula see VoseCopulaMultiGumbel.

### Example: correlating variables with a bivariate Gumbel copula

So for example, to generate a normal(0,1) and a beta(2,1) value correlated by a Gumbel(10) copula, you would do the following:

• Select the A1 and B1 spreadsheet cells.

• Type =VoseCopulaBiGumbel(10) in the Excel formula bar and press CTRL+SHIFT+ENTER - Excel now inserts this as an array function over the two selected cells, indicated by curly brackets.

• Insert =VoseNormal(0,1,A1) in the cell A2, and =VoseBeta(2,1, B1) in the cell B2. The cell references are U parameters that refer to the copula values generated in the first cell.

• Now the A2 and B2 cell contain random values correlated by the Gumbel(10) copula.

##### VoseFunctions for this copula

VoseCopulaBiGumbel generates values from this distribution or calculates a percentile.

VoseCopulaBiGumbelFit fits this copula to data.

VoseCopulaBiGumbelFitP returns the parameter(s) of this copula fitted to data.