SkewGedDistribution {fSeries}R Documentation

Symmetric and Skew Generalized Error Distribution

Description

A collection and description of functions to compute density, distribution function, quantile function and to generate random variates for the symmetric and skew generalized error distribution.

The functions are:

[dpqr]ged Symmetric GED distribution,
[dpqr]sged Skew GED distribution.

Usage

dged(x, mean = 0, sd = 1, nu = 2)
pged(q, mean = 0, sd = 1, nu = 2)
qged(p, mean = 0, sd = 1, nu = 2)
rged(n, mean = 0, sd = 1, nu = 2)

dsged(x, mean = 0, sd = 1, nu = 2, xi = 1.5)
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 number of observations.
p a numeric vector of probabilities.
x, q a numeric vector of quantiles.

Details

Symmetric GED Distibution:

The generalized error distribution functions are defined as described by Nelson (1991).

Skewed GED Distribution:

The skew generalized error distribution functions are defined as described by Fernandez and Steel (2000).

Value

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

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.

See Also

sstdDisytribution, snormDistribution.

Examples

## sged -
   xmpSeries("\nStart: Skew Generalized Error Distribuion:  > ")
   par(mfrow = c(2, 2), cex = 0.75)
   set.seed(1953)
   r = rsged(n = 1000, mean = 1, sd = 0.5, xi = 1.5)
   plot(r, type = "l", main = "sged: xi = 1.5")
   # Plot empirical density and compare with true density:
   hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue4")
   x = seq(-1, 5, 0.1)
   lines(x, dsged(x = x, mean = 1, sd = 0.5, xi = 1.5))
   # Plot df and compare with true df:
   plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue4")
   lines(x, psged(x, mean = 1, sd = 0.5, xi = 1.5))
   # Compute quantiles:
   qsged(psged(q = -1:5, mean = 1, sd = 0.5, xi = 1.5), 
     mean = 1, sd = 0.5, xi = 1.5) 

[Package fSeries version 200.10058 Index]