fGarch (version 290.76)

sged: 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: ll{ [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.

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.

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.

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)

## sgedSlider -
   if (require(tcltk)) {
   sgedSlider("dist")
   sgedSlider("rand")
   }