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

TL;DR

This paper introduces an alternative, more tractable representation of the Negative Binomial--Lindley distribution, enhancing its applicability across various fields with overdispersed data.

Contribution

It proposes a new formulation of the distribution with advantageous properties, including derivation of recurrence relations and integral equations, and discusses estimation methods with a numerical example.

Findings

New distribution representation with improved properties

Derived recurrence relations and integral equations

Demonstrated estimation methods with a numerical example

Abstract

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.