GeneralizedHyperbolicDistribution: The Package 'GeneralizedHyperbolic': Summary Information

In GeneralizedHyperbolic: The Generalized Hyperbolic Distribution

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 from package DistributionUtils. Q-Q and P-P plots are also provided for assessing the fit of a hyperbolic distribution. A Cramér-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 Würtz without whose advice, this package would be far inferior.

LICENCE

This package and its documentation are usable under the terms of the "GNU General Public License", a copy of which is distributed with the package.

Author(s)

David Scott [e-mail]

References

Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond., A353, 401–419.

Barndorff-Nielsen, O. and Blæsild, 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.

Jörgensen, 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.

GeneralizedHyperbolic documentation built on Nov. 26, 2023, 3 p.m.