R: Generalized Hyperbolic Student-t

ght {fBasics} | R Documentation

## Generalized Hyperbolic Student-t

### Description

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

`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

    ## ght -
       #

[Package fBasics version 3042.89 Index]