ghyp-package {ghyp}R Documentation

A package on generalized hyperbolic distributions

Description

Description: This package provides all about univariate and multivariate generalized hyperbolic distributions and its special cases (Hyperbolic (hyp), Normal Inverse Gaussian (NIG), Variance Gamma (VG) and skewed Student-t distribution). Especially fitting procedures, an AIC-based model selection routine and functions for the computation of the density, quantile, probability, random variates, expected shortfall and some portfolio optimization and plotting routines. In addition the generalized inverse gaussian distribution is contained in this package.

Details

Package: ghyp
Type: Package
Version: 0.9.3; svn-revision 132
Date: 2007-07-05
License: GPL (GNU Public Licence), Version 2 or later

Initialize:
ghyp Initialize a generalized hyperbolic distribution
hyp Initialize a hyperbolic distribution
NIG Initialize a normal inverse gaussian distribution
VG Initialize a variance gamma distribution
student.t Initialize a student-t distribution

Density, distribution function, quantile function, expected shortfall and random generation:
dghyp Density of a generalized hyperbolic distribution
pghyp Distribution function of a generalized hyperbolic distribution
qghyp Quantile of a univariate generalized hyperbolic distribution
ESghyp Expected shortfall of a univariate generalized hyperbolic distribution
rghyp Random generation of a generalized hyperbolic distribution

Fit to data:
fit.ghypuv Fit a generalized hyperbolic distribution to univariate data
fit.hypuv Fit a hyperbolic distribution to univariate data
fit.NIGuv Fit a normal inverse gaussian distribution to univariate data
fit.VGuv Fit a variance gamma distribution to univariate data
fit.tuv Fit a skewed student-t distribution to univariate data
fit.ghypmv Fit a generalized hyperbolic distribution to multivariate data
fit.hypmv Fit a hyperbolic distribution to multivariate data
fit.NIGmv Fit a normal inverse gaussian distribution to multivariate data
fit.VGmv Fit a variance gamma distribution to multivariate data
fit.tmv Fit a skewed student-t distribution to multivariate data
stepAIC.ghyp Perform a model selection based on the AIC

Portfolio optimization and utilities:
portfolio.optimize Calculate an optimal portfolio given a multivariate ghyp distribution
mean Returns the expected value
vcov Returns the variance in the univariate case or else the variance covariance matrix
logLik Returns Log-Likelihood of fitted ghyp objects.
AIC Returns Akaike's Information Criterion of fitted ghyp objects.
redim Extract certain dimensions of a multivariate ghyp distribution
lin.transf Transform a multivariate generalized hyperbolic distribution
ghyp.moment Moments of the univariate ghyp distribution
ghyp.params Parameters of a generalized hyperbolic distribution
ghyp.data Data of a (fitted) generalized hyperbolic distribution
ghyp.fit.info Information about the fitting procedure, log-likelihood and AIC value

Plot functions:
qqghyp Perform a quantile-quantile plot of a (fitted) univariate ghyp distribution
hist Plot a histogram of a (fitted) univariate generalized hyperbolic distribution
pairs Produce a matrix of scatterplots with quantile-quantile plots on the diagonal.

Generalized inverse gaussian distribution:
dgig Density of a generalized inverse gaussian distribution
pgig Distribution function of a generalized inverse gaussian distribution
qgig Quantile of a generalized inverse gaussian distribution
ESgig Expected shortfall of a generalized inverse gaussian distribution
rgig Random generation of a generalized inverse gaussian distribution

Package vignette:
A document about generalized hyperbolic distributions can be found in the doc folder of this package.

Existing solutions

There are already two packages HyperbolicDist and fBasics which cover univariate generalized hyperbolic distributions. However, the univariate case is contained in this package as well because we aim to provide a uniform interface to deal with generalized hyperbolic distribution. Recently an R port of the S-Plus library QRMlib was released. The package QRMlib contains fitting procedure for the NIG, hyp and skewed Student-t case but not for the generalized hyperbolic case. The package fMultivar implements a fitting routine for multivariate skewed student-t distributions as well. The table below gives an overview of available packages concerning generalized hyperbolic distributions and their capabilities.

ghyp Hyperbolic fBasics QRMlib multi_GHD
Dist (R & S-Plus) (Matlab)

Univariate:

Density x x x
Distribution x x x
Quantile x x x
Random Generation x x x
GH special cases hyp, NIG, hyp, VG hyp, NIG
VG, skew-t
Fit x only hyp x
Constant parameters x

Multivariate:

Density x x x
Distribution x
Random Generation x x x
GH special cases hyp, NIG, hyp, NIG
VG, skew-t
Fit x only hyp, NIG, skew-t x
Constant parameters x

Diagnostic plots:

hist x x x
Quantile-quantile x x
pairs x

Object orientation

We follow an object-oriented programming approach in this package and introduce distribution objects. There are mainly four reasons for that:

Author(s)

Wolfgang Breymann, David Lüthi

Institute of Data Analyses and Process Design (http://www.idp.zhwin.ch)

Maintainer: David Lüthi <david.luethi@zhwin.ch>

References

Quantitative Risk Management: Concepts, Techniques and Tools by Alexander J. McNeil, Rüdiger Frey and Paul Embrechts
Princeton Press, 2005

S-Plus and R Library for Quantitative Risk Management QRMlib by Alexander J. McNeil (2005) and Scott Ulman (R-port) (2007)
http://www.math.ethz.ch/~mcneil/book/QRMlib.html and QRMlib


[Package ghyp version 0.9.3 Index]