R: Skew GED Distribution and Parameter Estimation

sged {fGarch}

R Documentation

Skew GED Distribution and Parameter Estimation

Description

Functions to compute density, distribution function, quantile function and to generate random variates for the generalized error distribution. In addition maximum likelihood estimators are available to fit the parameters of the distribution.

The functions are:

`[dpqr]ged`	Symmetric GED Distribution,
`[dpqr]sged`	Skew GED Distribution,
`gedFit`	MLE parameter fit for a GED distribution,
`sgedFit`	MLE parameter fit for a skew GED distribution,
`sgedSlider`	Displays interactively 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)

gedFit(x, ...)
sgedFit(x, ...)

sgedSlider(type = c("dist", "rand"))

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.
`type`	a character string denoting which interactive plot should be displayed. Either a distribution plot `type="dist"`, the default value, or a random variates plot, `type="rand"`.
`x, q`	a numeric vector of quantiles.
`...`	parameters parsed to the optimization function `nlm`.

Details

Parameter Estimation:

The function nlm is used to minimize the "negative" maximum log-likelihood function. nlm carries out a minimization using a Newton-type algorithm.

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.

[s]gedFit returns a list with the following components:

`par`	The best set of parameters found.
`objective`	The value of objective corresponding to `par`.
`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.

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.

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)
       
## sgedFit -
   sgedFit(r)

## Not run:   
## sgedSlider -
   if (require(tcltk)) {
   sgedSlider("dist")
   sgedSlider("rand")
   }

## End(Not run)

[Package fGarch version 2110.80.1 Index]