Generalized Hyperbolic Student-t distribution

Density, distribution function, quantile function and random generation for the generalized hyperbolic Student-t distribution.

Usage

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

x, q

a numeric vector of quantiles.

p

a numeric vector of probabilities.

n

number of observations.

beta

numeric value, the skewness parameter in the range (0, alpha).

delta

numeric value, the scale parameter, must be zero or positive.

mu

numeric value, the location parameter, by default 0.

nu

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

log

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

Details

dght gives the density, pght gives the distribution function, qght gives the quantile function, and rght generates random deviates.

The parameters are as in the first parameterization.

Value

numeric vector

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

## ght -
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