# Skew Student-t distribution

`dist-sstd.Rd`

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

`TRUE`

, densities are given as log densities.

## 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.

## 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)
#> [1] -1 0 1 2 3 4 5
```