On modified discrete Pareto model: properties and applications

We present a discrete probability model, supported by non-negative integers, which generalizes the discrete Pareto distribution and provide better fit than the discrete Pareto distribution and some of its known generalizations. Various statistical properties like hazard rate function, crude moments, index of dispersion, skewness, kurtosis, L-moments, and entropies are derived. The proposed model exhibits the property of under-, equi- and over- dispersion. The new distribution has decreasing and upside-down bathtub failure rate function depending on its parameters. Following the theoretical introduction of this new discrete model, model parameters are estimated through maximum likelihood estimation, with a subsequent discussion on the performance of this technique through a simulation study. Finally, two real-world applications employing count data demonstrate the significance and adaptability of this distribution.