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).