dGHD: Density of a generalized hyperbolic distribution (GHD).

In MixGHD: Model Based Clustering, Classification and Discriminant Analysis Using the Mixture of Generalized Hyperbolic Distributions

Density of a generalized hyperbolic distribution (GHD).

Description

Compute the density of a p dimensional generalized hyperbolic distribution.

Usage

dGHD(data,p, mu=rep(0,p),alpha=rep(0,p),sigma=diag(p),omega=1,lambda=0.5, log=FALSE)

Arguments

data	n x p data set
p	number of variables.
mu	(optional) the p dimensional mean
alpha	(optional) the p dimensional skewness parameter alpha
sigma	(optional) the p x p dimensional scale matrix
omega	(optional) the unidimensional concentration parameter omega
lambda	(optional) the unidimensional index parameter lambda
log	(optional) if TRUE returns the log of the density

Details

The default values are: 0 for the mean and the skweness parameter alpha, diag(p) for sigma, 1 for omega, and 0.5 for lambda.

Value

A n dimensional vector with the density from a generilzed hyperbolic distribution

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <[e-mail]>

References

R.P. Browne, and P.D. McNicholas (2015). A Mixture of Generalized Hyperbolic Distributions. Canadian Journal of Statistics, 43.2 176-198

Examples

x = seq(-3,3,length.out=50)
y = seq(-3,3,length.out=50)
xyS1 = matrix(0,nrow=length(x),ncol=length(y))
for(i in 1:length(x)){
  for(j in 1:length(y)){
      xy <- matrix(cbind(x[i],y[j]),1,2)	
      xyS1[i,j] =  dGHD(xy,2) 
      
    }
  }
contour(x=x,y=y,z=xyS1, levels=c(.005,.01,.025,.05, .1,.25), main="MGHD",ylim=c(-3,3), xlim=c(-3,3))

MixGHD documentation built on May 11, 2022, 5:12 p.m.