In this paper, we have introduced a weighted model of the Quasi Lindley Distribution (QLD) as a new generalization of QLD. Statistical properties of this new distribution are derived and the model parameters are estimated by Maximum Likelihood (ML) estimation technique. Finally, the model is examined with an application to real life data.

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The article presents a new probability distribution, created by compounding the Poisson distribution with the weighted exponential distribution. Important mathematical and statistical properties of the distribution have been derived and discussed. The paper describes the proposed model's parameter estimation, performed by means of the maximum likelihood method. Finally, real data sets are analyzed to verify the suitability of the proposed distribution in modeling count data sets representing vaccine adverse events and insurance claims.