On the computer generation of the Erlang and negative binomial distributions with shape parameter equal to two (Q1005206)

The authors provide closed-form expressions for the quantile functions of the Erlang and negative binomial distributions with shape parameter equal to two. From a computational point of view, since the Lambert W function is efficiently implemented in various computer algebra systems -- Mathematica and Matlab, for instance -- both quantile functions can be evaluated with high accuracy in a straightforward manner.