| sstd {fGarch} | R Documentation |
Functions to compute density, distribution function,
quantile function and to generate random variates
for the standardized skew Student-t distribution. In
addition maximum likelihood estimators are available to
fit the parameters of the distribution.
The functions are:
[dpqr]std | Symmetric Student-t Distribution, |
[dpqr]sstd | Skew Student-t Distribution, |
stdFit | MLE parameter fit for a Sudent-t distribution, |
sstdFit | MLE parameter fit for a skew Sudent-t distribution, |
sstdSlider | Displays interactively skew GED distribution. |
dstd(x, mean = 0, sd = 1, nu = 5)
pstd(q, mean = 0, sd = 1, nu = 5)
qstd(p, mean = 0, sd = 1, nu = 5)
rstd(n, mean = 0, sd = 1, nu = 5)
dsstd(x, mean = 0, sd = 1, nu = 5, xi = 1.5)
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)
stdFit(x, ...)
sstdFit(x, ...)
sstdSlider(type = c("dist", "rand"))
mean, sd, nu, xi |
location parameter |
n |
the number of observations. |
p |
a numeric vector of probabilities. |
type |
a character string denoting which interactive plot should
be displayed. Either a distribution plot |
x, q |
a numeric vector of quantiles. |
... |
parameters parsed to the optimization function |
Parameter Estimation:
The function nlminb is used to minimize the "negative"
maximum log-likelihood function. nlminb carries out a
minimization using a Newton-type algorithm.
d* returns the density,
p* returns the distribution function,
q* returns the quantile function, and
r* generates random deviates,
all values are numeric vectors.
[s]stdFit returns a list with the following components:
par |
The best set of parameters found. |
objective |
The value of objective corresponding to |
convergence |
An integer code. 0 indicates successful convergence. |
message |
A character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation. |
iterations |
Number of iterations performed. |
evaluations |
Number of objective function and gradient function evaluations. |
Diethelm Wuertz for the Rmetrics R-port.
Fernandez C., Steel M.F.J. (2000); On Bayesian Modelling of Fat Tails and Skewness, Preprint, 31 pages.
## 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)
## sstdFit -
sstdFit(r, print.level = 2)