The new Poisson mixed weighted Lindley distribution with applications to insurance claims data

Abstract

Mixed Poisson distributions have been applied for overdispersed count data analysis. In this paper, an alternative mixed Poisson distribution is proposed. The proposed distribution is derived by mixing the Poisson distribution with the new weighted Lindley distribution, named as the new Poisson mixed weighted Lindley distribution. Some special cases and several statistical properties have been derived including shape, factorial moments, probability generating function, moment generating function and moments. The maximum likelihood estimators of the parameters are obtained. Finally, two automobile insurance claims data sets are analyzed to compare the performance of the proposed distribution with some competitive distributions.

Keywords

• count data
• overdispersion
• new weighted lindley distribution
• mixed poisson distribution
• maximum likelihood estimation