XploRe Help : VaRcumulantsDG

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	VaR
See also:	VaRcumulantDG

Quantlet:		VaRcumulantsDG
Description:		compute the first n cumulants for the class of quadratic forms of Gaussian vectors.

Reference(s):

Jaschke, S. (2001). The Cornish-Fisher-Expansion in the Context of Delta-Gamma-Normal Approximations.

Link:

Cornish-Fisher-Expansion

Usage:	`r = VaRcumulantsDG(n,l)`
Input:
	`n`	scalar, highest order of cumulants to be computed
	`l`	a list defining the distribution; contains at least the following components: theta - the constant term Delta - the linear term (the first derivative) Gamma - the quadratic term (the Hessian matrix) Sigma - the covariance matrix
Output:
	`r`	n x 1 vector of the first n cumulants

Note:

This function does not need the initial diagonalization. If the diagonalization has been done already, use VaRcumulantDG, which is faster.

Example:

library("VaR") library("xplore") theta = 0 Delta = #(1) Gamma = unit(1) Sigma = unit(1) par = list(theta,Delta,Gamma,Sigma) VaRcumulantsDG(4,par)

Result:

Contents of r
[1,]      0.5
[2,]      1.5
[3,]        4
[4,]       15

Author: S. Jaschke, 20011026 license MD*Tech