A note on the computer generation of the binomial exponential distribution and generalizations

Abstract

The binomial exponential distribution as well as its generalizations power binomial exponential and generalized binomial exponential have been introduced in the statistical literature as more flexible models than other probability distributions with support on the positive real line. Different algorithms have been proposed to generate by computer random samples from these new distributions. In this note, it is shown that the quantile functions of the three aforementioned distributions can be written analytically in terms of the Lambert W function. As a consequence, random samples from these families of distributions can be generated more easily from closed-form formulae.