urt {Runuran} | 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.
[Distribution] – Sampling Function: t (Student).
urt(n, df, lb = -Inf, ub = Inf)
n |
size of required sample. |
df |
degrees of freedom (> 0, maybe non-integer). |
lb |
lower bound of (truncated) distribution. |
ub |
upper bound of (truncated) distribution. |
The t distribution with df
= n degrees of
freedom has density
f(x) = Gamma((n+1)/2) / (sqrt(n pi) Gamma(n/2)) (1 + x^2/n)^-((n+1)/2)
for all real x. It has mean 0 (for n > 1) and variance n/(n-2) (for n > 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-wien.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)