dsmghyp {QRMlib}R Documentation

Symmetric Multivariate Generalized Hyperbolic Distribution

Description

Density of elliptical subfamily of multivariate generalized hyperbolic family. The symmetric family is a normal-variance mixture since the gamma parameter associated with the mean mixture is by assumption equal to zero.

Usage

dsmghyp(x, lambda, chi, psi, mu, Sigma, logvalue=FALSE)

Arguments

x matrix with n rows and d columns; density is evaluated at each vector of row values
lambda scalar parameter
chi scalar parameter
psi scalar parameter
mu location vector
Sigma dispersion matrix
logvalue should log density be returned; default is FALSE

Details

See page 78 in QRM for joint density formula (3.30) with Sigma a d-dimensional dispersion matrix (d > 1) consistent with a multivariate distribution). This is a more intuitive parameterization of the alpha-beta-delta model used by Blaesild (1981) in earlier literature since it associates all parameters with mixtures of both mean and variance. Since gamma is 0, we have a normal-variance mixture where the mixing variable W has a GIG generalized inverse gaussian) distribution with parameters lambda, chi, psi. This thickens the tail.

Since gamma equals zero, we have no perturbation of the mean so no ASYMMETRY is introduced and hence the distribution is symmetric.

There is no random number generation associated with the multivariate model in this implementation of the R-language and S-Plus code.

See pp. 77-81 of QRM and appendix A.2.5 for details.

dsmghyp() is frequently called from the function dmghyp().

Value

vector of length n containing values of density or log-density

Author(s)

documentation by Scott Ulman for R-language distribution

See Also

dmghyp

Examples

## Not run: 
dmghyp <- function(x, lambda, chi, psi, mu, Sigma, gamma,logvalue=FALSE)
{
  #Call symmetric form if gamma vector is identically zero:
  if (sum(abs(gamma))==0) 
       out <- dsmghyp(x, lambda,chi,psi,mu,Sigma,logvalue=TRUE);
  # lines removed here
}
## End(Not run)

[Package QRMlib version 1.4.4 Index]