VolElliptope {fungible}

Compute the volume of the elliptope of possible correlation matrices of a given dimension.

Description

Compute the volume of the elliptope of possible correlation matrices of a given dimension.

Usage

VolElliptope(NVar)

Arguments

NVar

(integer) The size of each correlation matrix in the elliptope. For instance, if we are interested in the volume of the space of all possible 5 x 5 correlation matrices then NVar = 5.

Value

VolElliptope returns the following objects:

• VolElliptope (numeric) The volume of the elliptope.

• VolCube: (numeric) The volume of the embedding hyper-cube.

• PrcntCube (numeric) The percent of the hyper-cube that is occupied by the elliptope. PrcntCube = 100 x VolElliptope/VolCube.

Author(s)

Niels G. Waller

References

Joe, H. (2006). Generating random correlation matrices based on partial correlations. *Journal of Multivariate Analysis*, *97* (10), 2177–2189.

Hürlimann, W. (2012). Positive semi-definite correlation matrices: Recursive algorithmic generation and volume measure. *Pure Mathematical Science, 1* (3), 137–149.

Examples

# Compute the volume of a 5 x 5 correlation matrix.

VolElliptope(NVar = 5)