A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical and reliability properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Anderson’s-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets “coronavirus-flood peaks-forest fire-Leukemia”. Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.