  In this paper we present an alternative representation of the Negative
Binomial--Lindley distribution recently proposed by Zamani and Ismail (2010)
which shows some advantages over the latter model. This new formulation
provides a tractable model with attractive properties which makes it suitable
for application not only in insurance settings but also in other fields where
overdispersion is observed. Basic properties of the new distribution are
studied. A recurrence for the probabilities of the new distribution and an
integral equation for the probability density function of the compound version,
when the claim severities are absolutely continuous, are derived. Estimation
methods are discussed and a numerical application is given.
