sstd {fGarch} | R Documentation |
Skew Student-t distribution
Description
Functions to compute density, distribution function, quantile function and to generate random variates for the skew Student-t distribution.
Usage
dsstd(x, mean = 0, sd = 1, nu = 5, xi = 1.5, log = FALSE)
psstd(q, mean = 0, sd = 1, nu = 5, xi = 1.5)
qsstd(p, mean = 0, sd = 1, nu = 5, xi = 1.5)
rsstd(n, mean = 0, sd = 1, nu = 5, xi = 1.5)
Arguments
x , q |
a numeric vector of quantiles. |
p |
a numeric vector of probabilities. |
n |
number of observations to simulate. |
mean |
location parameter. |
sd |
scale parameter. |
nu |
shape parameter (degrees of freedom). |
xi |
skewness parameter. |
log |
logical; if |
Details
The distribution is standardized as discussed in the reference by Wuertz et al below.
dsstd
computes the density,
psstd
the distribution function,
qsstd
the quantile function, and
rsstd
generates random deviates.
Value
numeric vector
Author(s)
Diethelm Wuertz for the Rmetrics R-port
References
Fernandez C., Steel M.F.J. (2000); On Bayesian Modelling of Fat Tails and Skewness, Preprint, 31 pages.
Wuertz D., Chalabi Y. and Luksan L. (????); Parameter estimation of ARMA models with GARCH/APARCH errors: An R and SPlus software implementation, Preprint, 41 pages, https://github.com/GeoBosh/fGarchDoc/blob/master/WurtzEtAlGarch.pdf
See Also
sstdFit
(fit),
sstdSlider
(visualize)
Examples
## sstd -
par(mfrow = c(2, 2))
set.seed(1953)
r = rsstd(n = 1000)
plot(r, type = "l", main = "sstd", col = "steelblue")
# Plot empirical density and compare with true density:
hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue")
box()
x = seq(min(r), max(r), length = 201)
lines(x, dsstd(x), lwd = 2)
# Plot df and compare with true df:
plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue",
ylab = "Probability")
lines(x, psstd(x), lwd = 2)
# Compute quantiles:
round(qsstd(psstd(q = seq(-1, 5, by = 1))), digits = 6)