Generalized Hyperbolic Student-t

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Description

Density, distribution function, quantile function and random generation for the hyperbolic distribution.

Usage

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dght(x, beta = 0.1, delta = 1, mu = 0, nu = 10, log = FALSE)
pght(q, beta = 0.1, delta = 1, mu = 0, nu = 10)
qght(p, beta = 0.1, delta = 1, mu = 0, nu = 10)
rght(n, beta = 0.1, delta = 1, mu = 0, nu = 10)

Arguments

beta, delta, mu

numeric values. beta is the skewness parameter in the range (0, alpha); delta is the scale parameter, must be zero or positive; mu is the location parameter, by default 0. These are the parameters in the first parameterization.

nu

a numeric value, the number of degrees of freedom. Note, alpha takes the limit of abs(beta), and lambda=-nu/2.

x, q

a numeric vector of quantiles.

p

a numeric vector of probabilities.

n

number of observations.

log

a logical, if TRUE, probabilities p are given as log(p).

Value

All values for the *ght functions are numeric vectors: d* returns the density, p* returns the distribution function, q* returns the quantile function, and r* generates random deviates.

All values have attributes named "param" listing the values of the distributional parameters.

References

Atkinson, A.C. (1982); The simulation of generalized inverse Gaussian and hyperbolic random variables, SIAM J. Sci. Stat. Comput. 3, 502–515.

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

Barndorff-Nielsen O., Blaesild, 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.

Raible S. (2000); Levy Processes in Finance: Theory, Numerics and Empirical Facts, PhD Thesis, University of Freiburg, Germany, 161 pages.

Examples

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## ght -
   #

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