HyperbolicDistribution: The Package 'HyperbolicDist': Summary Information In HyperbolicDist: The Hyperbolic Distribution

 HyperbolicDistribution R Documentation

The Package ‘HyperbolicDist’: Summary Information

Description

This package provides a collection of functions for working with the 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 parameterisations. 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 Crämer-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 parameterisations. 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 parameterisations. 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, and Thomas Tran.

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.

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.

Author(s)

David Scott d.scott@auckland.ac.nz

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.

HyperbolicDist documentation built on Nov. 26, 2023, 9:07 a.m.