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).
Usage
urt(n, df, lb = -Inf, ub = Inf)
Arguments
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.
Details
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).
References
W. H"ormann, J. Leydold, and G. Derflinger (2004):
Automatic Nonuniform Random Variate Generation.
Springer-Verlag, Berlin Heidelberg
See Also
runif and .Random.seed about random number
generation, unuran for the UNU.RAN class, and
rt for the Rbuilt-in generator.