dist-skstd: Skew Student's t Distribtuion from Fernandez and Steel (1997)

In GEVStableGarch: ARMA-GARCH/APARCH Models with GEV and Stable Distributions

Description

Functions to compute density, distribution function, quantile function and to generate random values for the Skew Student's t distribtuion from Fernandez and Steel (1997). Notice that this function is different from the skew Student's t sstd from package fGarch. Although the two distributions use the same approach from Fernandez and Steel (1997), the second one was reparameterized in such a way that when the parameters mean = 0 and sd = 1 the distribution will have a zero mean and unit variance, no matter the value of the skew parameter. The distributions skstd and sstd are the same when the asymmetry parameter xi equals to 1, in which case they correspond to the well known Student's t distribution std.

Usage

dskstd(x, mean = 0, sd = 1, nu = 3, xi = 1, log = FALSE)
pskstd(q, mean = 0, sd = 1, nu = 3, xi = 1)
qskstd(p, mean = 0, sd = 1, nu = 3, xi = 1)
rskstd(n, mean = 0, sd = 1, nu = 3, xi = 1)

Arguments

mean, sd, nu, xi	location parameter mean, scale parameter sd, shape parameter nu, asymmetry 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.

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)

Thiago do Rego Sousa.

References

Fernandez, C., Steel, M.F. (1998). On Bayesian Modeling of Fat Tails and Skewness. Journal of the American Statistical Association, Taylor & Francis Group, 93(441), 359–371.

Examples

# Simulate Random Values and compare with
# the empirical density and probability functions
# Note: This example was addapted from "sstd {fGarch} R Documentation"

# Configure plot and generate random values
par(mfrow = c(2, 2))
set.seed(1000)
r = rskstd(n = 1000)
plot(r, type = "l", main = "Skew Student's t Random Values", 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, dskstd(x), lwd = 2)

# Plot density function and compare with true df:
plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue",
     ylab = "Probability")
lines(x, pskstd(x), lwd = 2)

# Compute quantiles:
# Here we compute the quantiles corresponding to the probability points from 
# -10 to 10 and expect to obtain the same input sequence
round(qskstd(pskstd(q = seq(-10, 10, by = 0.5))), digits = 6)

GEVStableGarch documentation built on May 2, 2019, 5:53 a.m.