fBasics (version 3011.87)

sght: Standardized generalized hyperbolic Student-t Distribution

Description

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

Usage

dsght(x, beta = 0.1, delta = 1, mu = 0, nu = 10, log = FALSE)
psght(q, beta = 0.1, delta = 1, mu = 0, nu = 10)
qsght(p, beta = 0.1, delta = 1, mu = 0, nu = 10)
rsght(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 *sght 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.

Examples

## rsght -
   set.seed(1953)
   r = rsght(5000, beta = 0.1, delta = 1, mu = 0, nu = 10)
   plot(r, type = "l", col = "steelblue",
     main = "gh: zeta=1 rho=0.5 lambda=1")

## dsght -
   # Plot empirical density and compare with true density:
   hist(r, n = 50, probability = TRUE, border = "white", col = "steelblue")
   x = seq(-5, 5, length = 501)
   lines(x, dsght(x, beta = 0.1, delta = 1, mu = 0, nu = 10))

## psght -
   # Plot df and compare with true df:
   plot(sort(r), (1:5000/5000), main = "Probability", col = "steelblue")
   lines(x, psght(x, beta = 0.1, delta = 1, mu = 0, nu = 10))

## qsght -
   # Compute Quantiles:
   round(qsght(psght(seq(-5, 5, 1), beta = 0.1, delta = 1, mu = 0, nu =10),
               beta = 0.1, delta = 1, mu = 0, nu = 10), 4)