SkewGedDistribution {fSeries} | R Documentation |
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. |
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)
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. |
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).
All values are numeric vectors:
d*
returns the density,
p*
returns the distribution function,
q*
returns the quantile function, and
r*
generates random deviates.
Diethelm Wuertz for the Rmetrics R-port.
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.
sstdDisytribution
,
snormDistribution
.
## 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)