dist-sged: Skew generalized error distribution

In fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling

Skew generalized error distribution

Description

Functions to compute density, distribution function, quantile function and to generate random variates for the skew generalized error distribution.

Usage

dsged(x, mean = 0, sd = 1, nu = 2, xi = 1.5, log = FALSE)
psged(q, mean = 0, sd = 1, nu = 2, xi = 1.5)
qsged(p, mean = 0, sd = 1, nu = 2, xi = 1.5)
rsged(n, mean = 0, sd = 1, nu = 2, xi = 1.5)

Arguments

mean, sd, nu, xi	location parameter mean, scale parameter sd, shape parameter nu, skewness parameter xi.
n	the number of observations.
p	a numeric vector of probabilities.
x, q	a numeric vector of quantiles.
log	a logical; if TRUE, densities are given as log densities.

Details

The distribution is standardized as discussed in the reference by Wuertz et al below.

Value

d* returns the density, p* returns the distribution function, q* returns the quantile function, and r* generates random deviates,
all values are numeric vectors.

Author(s)

Diethelm Wuertz for the Rmetrics R-port

References

Nelson D.B. (1991); Conditional Heteroscedasticity in Asset Returns: A New Approach, Econometrica, 59, 347–370.

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

sgedFit (fit), sgedSlider (visualize),

ged (symmetric GED)

Examples

## sged -
   par(mfrow = c(2, 2))
   set.seed(1953)
   r = rsged(n = 1000)
   plot(r, type = "l", main = "sged", 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, dsged(x), lwd = 2)
   
   # Plot df and compare with true df:
   plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue",
     ylab = "Probability")
   lines(x, psged(x), lwd = 2)
   
   # Compute quantiles:
   round(qsged(psged(q = seq(-1, 5, by = 1))), digits = 6)

fGarch documentation built on May 29, 2024, 8:30 a.m.