urt | R Documentation |
UNU.RAN random variate generator for the Student t distribution with
with df
degrees of freedom.
It also allows sampling from the truncated distribution.
[Special Generator] – Sampling Function: t (Student).
urt(n, df, lb = -Inf, ub = Inf)
n |
size of required sample. |
df |
degrees of freedom ( |
lb |
lower bound of (truncated) distribution. |
ub |
upper bound of (truncated) distribution. |
The t
distribution with df
= \nu
degrees of
freedom has density
f(x) = \frac{\Gamma ((\nu+1)/2)}{\sqrt{\pi \nu} \Gamma (\nu/2)}
(1 + x^2/\nu)^{-(\nu+1)/2}%
for all real x
.
It has mean 0
(for \nu > 1
) and
variance \frac{\nu}{\nu-2}
(for \nu > 2
).
The generation algorithm uses fast numerical inversion. The parameters
lb
and ub
can be used to generate variates from
the t
distribution truncated to the interval (lb
,ub
).
This function is a wrapper for the UNU.RAN class in R.
Compared to rt
, urt
is faster, especially for
larger sample sizes.
However, in opposition to rt
vector arguments are ignored,
i.e. only the first entry is used.
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg
runif
and .Random.seed
about random number
generation, unuran
for the UNU.RAN class, and
rt
for the R built-in generator.
## Create a sample of size 1000
x <- urt(n=1000,df=4)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.