R: Standardized generalized hyperbolic Student-t Distribution
sght
R Documentation
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.
Author(s)
Diethelm Wuertz.
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)