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 Rport 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. 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
}
rand(n, distribution.object.
Additionally, one can take advantage of generic programming sinceRprovides virtual
classes and some forms of polymorphism.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.
QRMlib