The Binomial distribution with size \(= n\) and
prob \(= p\) has density
$$
p(x) = {n \choose x} {p}^{x} {(1-p)}^{n-x}
$$
for \(x = 0, \ldots, n\).
The generation algorithm uses guide table based inversion. The parameters
lb and ub can be used to generate variates from
the Binomial distribution truncated to the interval (lb,ub).