The hyperbolic distribution

This package provides functions for the hyperbolic and related distributions. Density, distribution and quantile functions and random number generation are provided for the hyperbolic distribution, the generalized hyperbolic distribution, the generalized inverse Gaussian distribution and the skew-Laplace distribution. Additional functionality is provided for the hyperbolic distribution, including fitting of the hyperbolic to data.


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o Some bug fixes added which were causing Make Check to fail on Windows when tested using Uwe Ligges site. Problem was naming of objects as x conflicting with use of x as data.


o Names changed to form with words after the initial one capitalized, e.g. becomes logPars. Applies to both function and variable names. Exceptions are functions for distributions (dhyperb, rgig, pskewlap), and KNu.

o Added functions for the skew-Laplace distribution: dskewlap, pskewlap, qskewlap and r skewlap.

o Added (xi, chi) parameterisation to those for which hyperbChangePars (which was can be used to interchange between parameterisations of the hyperbolic distribution.

o Added functions for the generalized hyperbolic distribution: dghyp, pghyp, qghyp, rghyp, ghypChangePars, ghypCalcRange, ghypMean, ghypVar, ghypMode.

o Added functions for the generalized inverse Gaussian distribution: dgig, pgig, qgig, rgig1, rgig, gigChangePars,gigCalcRange, gigMean, gigVar, gigSkew, gigKurt, gigMode.

o Parameter vector name changed to Theta instead of theta so an individual component could be called theta.

o New algorithms developed for phyperb, pghyp, and pgig where numerical integrations are on sections of the real line. Developed to improve accuracy of numerical results.

o New algorithms for distribution functions use the derivative of the density and need break points to determine sections to integrate over. Derivative functions ddhyperb, ddghyp, ddgig, and break functions hyperbBreaks, ghypBreaks, gigBreaks developed.

o Functions for Cramer-von Mises goodness of fit test for the hyperbolic distribution added.


o Submitted to CRAN, January 6, 2003

Reference manual

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0.6-2 by David Scott, 12 years ago

Browse source code at

Authors: David Scott <[email protected]>

Documentation:   PDF Manual  

Task views: Probability Distributions

GPL (>= 2) license

Suggests VarianceGamma, actuar

Imported by ALDqr, NormalBetaPrime, exdqlm.

Suggested by fitteR.

See at CRAN