public virtual double[] NextStudentsTCopula(
	double df,
	Cholesky chol
)

Public Overridable Function NextStudentsTCopula ( 
	df As Double,
	chol As Cholesky
) As Double()

public:
virtual array<double>^ NextStudentsTCopula(
	double df, 
	Cholesky^ chol
)

abstract NextStudentsTCopula : 
        df : float * 
        chol : Cholesky -> float[] 
override NextStudentsTCopula : 
        df : float * 
        chol : Cholesky -> float[] 

Parameters

df

Type: SystemDouble
A double which specifies the degrees of freedom parameter.

chol

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

Return Value

NextStudentsTCopula generates pseudorandom numbers from a multivariate Student's t Copula distribution which are uniformly distributed on the interval (0,1) representing the probabilities associated with deviates from Student's t distributions with df degrees of freedom imprinted with correlation information from the 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 Student's t deviates with mean 0 and df degrees of freedom is generated, and then this deviate vector is post-multiplied by Cholesky matrix R. Finally, the Cholesky-imprinted random Student's t deviates are mapped to output probabilities using the Student's t cumulative distribution function (CDF) with df degrees of freedom.

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