A note on the Log-Lindley distribution

The Log-Lindley distribution is a continuous probability model with useful applications in insurance and inventory management. In this note, it is proven that pseudo-random data from this model can be generated by computer via the Lambert W function. A reparametrization suitable to get estimates of the parameters is proposed. Moreover, it is shown that this reparametrization is appropriate to perform a regression analysis with dependent variable taking values in the unit interval.