R: The Package 'GeneralizedHyperbolic': Summary Information
GeneralizedHyperbolic
R Documentation
The Package ‘GeneralizedHyperbolic’: Summary Information
Description
This package provides a collection of functions for working with the generalized
hyperbolic and related distributions.
For the hyperbolic distribution functions are provided for the density
function, distribution function, quantiles, random number generation and
fitting the hyperbolic distribution to data (hyperbFit). The
function hyperbChangePars will interchange parameter values
between different parameterizations. The mean, variance, skewness,
kurtosis and mode of a given hyperbolic distribution are given by
hyperbMean, hyperbVar, hyperbSkew,
hyperbKurt, and hyperbMode respectively. For assessing the
fit of the hyperbolic distribution to a set of data, the log-histogram
is useful. See logHist. Q-Q and P-P
plots are also provided for assessing the fit of a hyperbolic
distribution. A Cr<c3><a4>mer-von~Mises test of the goodness of
fit of data to a hyperbolic distribution is given by
hyperbCvMTest. S3 print, plot and summary
methods are provided for the output of hyperbFit.
For the generalized hyperbolic distribution functions are provided for
the density function, distribution function, quantiles, and for random
number generation. The function ghypChangePars will interchange
parameter values between different parameterizations. The mean, variance, and
mode of a given generalized hyperbolic distribution are given by
ghypMean, ghypVar, ghypSkew, ghypKurt, and
ghypMode respectively. Q-Q and P-P plots are also provided for
assessing the fit of a generalized hyperbolic distribution.
For the generalized inverse Gaussian distribution functions are provided for
the density function, distribution function, quantiles, and for random
number generation. The function gigChangePars will interchange
parameter values between different parameterizations. The mean,
variance, skewness, kurtosis and mode of a given generalized inverse
Gaussian distribution are given by gigMean, gigVar,
gigSkew, gigKurt, and gigMode respectively. Q-Q and
P-P plots are also provided for assessing the fit of a generalized
inverse Gaussian distribution.
For the skew-Laplace distribution functions are provided for
the density function, distribution function, quantiles, and for random
number generation. Q-Q and P-P plots are also provided for assessing the
fit of a skew-Laplace distribution.
Acknowledgements
A number of students have worked on the package: Ai-Wei Lee, Jennifer Tso,
Richard Trendall, Thomas Tran, Simon Potter and David Cusack.
Thanks to Ross Ihaka and Paul Murrell for their willingness to answer
my questions, and to all the core group for the development of R.
Special thanks also to Diethelm W<c3><bc>rtz without whose
advice, this package would be far inferior.
LICENCE
This library and its documentation are usable under the terms of the
"GNU General Public License", a copy of which is distributed with the
package.
Barndorff-Nielsen, O. (1977)
Exponentially decreasing distributions for the logarithm of particle size,
Proc. Roy. Soc. Lond.,
A353, 401–419.
Barndorff-Nielsen, O. and Bl<c3><a6>sild, P (1983).
Hyperbolic distributions.
In Encyclopedia of Statistical Sciences,
eds., Johnson, N. L., Kotz, S. and Read, C. B., Vol. 3,
pp. 700–707. New York: Wiley.
Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992)
Statistics of particle size data.
Appl. Statist.,
41, 127–146.
J<c3><b6>rgensen, B. (1982). Statistical Properties of
the Generalized Inverse Gaussian Distribution. Lecture Notes in
Statistics, Vol. 9, Springer-Verlag, New York.
Prause, K. (1999)
The generalized hyperbolic models: Estimation, financial
derivatives and risk measurement. PhD Thesis, Mathematics Faculty,
University of Freiburg.