public virtual double[] NextGaussianCopula(
	Cholesky chol
)

Public Overridable Function NextGaussianCopula ( 
	chol As Cholesky
) As Double()

public:
virtual array<double>^ NextGaussianCopula(
	Cholesky^ chol
)

abstract NextGaussianCopula : 
        chol : Cholesky -> float[] 
override NextGaussianCopula : 
        chol : Cholesky -> float[] 

Parameters

chol

Type: Imsl.MathCholesky
A Cholesky object containing the Cholesky factorization of the correlation matrix of order k.

Return Value

NextGaussianCopula generates pseudorandom numbers from a multivariate Gaussian Copula distribution which are uniformly distributed on the interval (0,1) representing the probabilities associated with N(0,1) deviates imprinted with correlation information from input Cholesky object chol. Cholesky matrix R is defined as the "square root" of a user-defined correlation matrix, that is R is an upper triangular matrix such that the transpose of R times R is the correlation matrix.

First, a length k vector of independent random normal deviates with mean 0 and variance 1 is generated, and then this deviate vector is post-multiplied by cholesky matrix R. Finally, the Cholesky-imprinted random N(0,1) deviates are mapped to output probabilities using the N(0,1) cumulative distribution function (CDF).

Random deviates from arbitrary marginal distributions which are imprinted with the correlation information contained in Cholesky matrix R can then be generated by inverting the output probabilities using user-specified inverse CDF functions.

Reference

Other Resources