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 domain of the distribution can be truncated to the
interval (lb,ub).
References
N.L. Johnson, S. Kotz, and N. Balakrishnan (1995):
Continuous Univariate Distributions, Volume 2.
2nd edition, John Wiley & Sons, Inc., New York.
Chap. 28, p. 362.
## Create distribution object for t distributiondistr <- udt(df=4)
## Generate generator object; use method PINV (inversion)gen <- pinvd.new(distr)
## Draw a sample of size 100x <- ur(gen,100)