dist-ght: Generalized Hyperbolic Student-t In fBasics: Rmetrics - Markets and Basic Statistics

Description

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

Usage

 1 2 3 4 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

 1 2 3 ## ght - #

fBasics documentation built on March 13, 2020, 9:09 a.m.