sstdDistribution {fSeries} | R Documentation |
A collection of functions to compute density, distribution function,
quantile function and to generate random variates for the symmetric
and skew Sudent-t distribution with unit variance.
The functions are:
1 | [dpqr]std | Symmetric Student-t Distribution, |
2 | [dpqr]sstd | Skew Student-t Distribution. |
dstd(x, mean = 0, sd = 1, nu = 5) pstd(q, mean = 0, sd = 1, nu = 5) qstd(p, mean = 0, sd = 1, nu = 5) rstd(n, mean = 0, sd = 1, nu = 5) dsstd(x, mean = 0, sd = 1, nu = 5, xi = 1.5) psstd(q, mean = 0, sd = 1, nu = 5, xi = 1.5) qsstd(p, mean = 0, sd = 1, nu = 5, xi = 1.5) rsstd(n, mean = 0, sd = 1, nu = 5, 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 Student-t Distibution:
The functions for the symmetric Student-t distribution are
rescaled in such a way that they have unit variance in
contrast to the Student-t family dt
, pt
,
qt
and rt
which are part of R's base package.
Skew Student-t Distribution:
The skew Student-t distribution functions are defined as described
by Fernandez and Steel (2000). Note that the function have unit
variance.
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 this R-port.
Fernandez C., Steel M.F.J. (2000); On Bayesian Modelling of Fat Tails and Skewness, Preprint, 31 pages.
snormDistribution
,
sgedDistribution
.
## sstd - xmpSeries("\nStart: Skew Student-t Distribuion: > ") par(mfrow = c(2, 2), cex = 0.75) set.seed(1953) r = rsstd(n = 1000, nu =4, xi = 1.5) # Print Variance: var(r) plot(r, type = "l", main = "sstd: xi = 1.5") # Plot empirical density and compare with true density: hist(r, n = 30, xlim = c(-5, 5), probability = TRUE, border = "white", col = "steelblue4") x = seq(-5, 5, 0.1) lines(x, dsnorm(x = x, xi = 1.5)) # Plot df and compare with true df: plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue4") lines(x, psstd(x, xi = 1.5)) # Compute quantiles: qsstd(psstd(q = -5:5, xi = 1.5), xi = 1.5)