Skew Student-t distribution

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.

Value

numeric vector

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

Author

Diethelm Wuertz for the Rmetrics R-port

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