Density, distribution function, quantile function and random generation for the hyperbolic distribution.
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)
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.
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.
a numeric value, the number of degrees of freedom.
Note, alpha takes the limit of abs(beta),
and lambda=-nu/2.
a numeric vector of quantiles.
a numeric vector of probabilities.
number of observations.
a logical, if TRUE, probabilities p are given as
log(p).
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.