A new discrete XLindley distribution: theory, actuarial measures, inference, and applications

This study proposes a discrete probability model for the modeling of count datasets. Some important properties are derived, including characteristic and moment-generating functions, mean, variance, index of dispersion, skewness, kurtosis, and risk measures (actuarial measures). The maximum likelihood estimation approach has been used to estimate parameter estimates for the proposed distribution. The convergence of the estimators is assessed via a simulation study. In the end, applications to four practical datasets are given to show the usefulness of the proposed distribution over famous discrete distributions. It is manifest that the proposed model provides a better fit than competitive models.