The Poisson distribution has density
$$
p(x) = \frac{\lambda^x e^{-\lambda}}{x!}
$$
for \(x = 0, 1, 2, \ldots\).
The generation algorithm uses guide table based inversion when the
tails are not too heavy and method ‘DARI’ otherwise.
The parameters lb and ub can be used to generate
variates from the Poisson distribution truncated to the interval
(lb,ub).