Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function

We provide procedures to generate random variables with Lindley distribution, and also with Poisson–Lindley or zero-truncated Poisson–Lindley distribution, as simple alternatives to the existing algorithms. Our procedures are based on the fact that the quantile functions of these probability distributions can be expressed in closed form in terms of the Lambert W function. As a consequence, the extreme order statistics from the above distributions can also be computer generated in a straightforward manner.