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

An alternative representation of the negative binomial-Lindley distribution. New results and applications