| Version: | 1.0 |
| Date: | 2021-12-10 |
| Title: | The Skewed Student-t Distribution |
| Description: | Density, distribution function, quantile function and random generation for the skewed t distribution of Fernandez and Steel. |
| License: | GPL-2 | GPL-3 [expanded from: GPL] |
| NeedsCompilation: | no |
| Packaged: | 2021-12-09 23:57:40 UTC; rober |
| Author: | Robert King  [aut,
cre],
Emily Anderson [aut] |
| Maintainer: | Robert King <Robert.King.newcastle@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2021-12-10 12:00:02 UTC |
The Skewed Student t Distribution
Description
Density, distribution function, quantile function and random
generation for the skewed t distribution, as introduced by Fernandez and
Steel, with df degrees of freedom.
Usage
dskt(x, df, gamma = 1)
pskt(x, df, gamma = 1)
qskt(p, df, gamma)
rskt(n, df, gamma)
Arguments
x |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
df |
degrees of freedom ( |
gamma |
skewing parameter, |
Details
The Skewed t distribution with df = \nu degrees of
freedom has the following density, where f(x) is the density of the
t distribution, with = \nu degrees of
freedom :
f(x) = \frac{2}{\gamma + \frac{1}{\gamma}} f(\gamma x) \quad for
\quad x<0
and
f(x) = \frac{2}{\gamma + \frac{1}{\gamma}} f(\frac{x}{\gamma}) \quad
for \quad x \ge 0
Value
dskt gives the density,
pskt gives the distribution function,
qskt gives the quantile function, and
rskt generates random deviates.
References
Fernandez, C. and Steel, M. F. J. (1998). On Bayesian modeling of fat tails and skewness, J. Am. Statist. Assoc. 93, 359–371.
Rohr, P. and Hoeschele, I. (2002).
Bayesian QTL mapping using skewed Student-t distributions,
Genet. Sel. Evol. 34, 1–21.
See Also
df for the F distribution.
Examples
dskt(0.5,2)
dskt(0.01,2,2)
pskt(1.25,2,2)
pskt(c(0.5,1.25),3)
qskt(c(0,0.025,0.25,0.5,0.75,0.975,1),2,2)
rskt(100,2,2)
plot(function(x)dskt(x,2,2),-3,3,n=301)