The discrete power-Ailamujia distribution: properties, inference, and applications

In this article, a new two-parameter discrete power-Ailamujia (DsPA) distribution is derived using the survival discretization technique. Some key distributional properties and reliability measures are explored in closed forms, such as probability generating function, first four moments and mean residual life. The DsPA parameters are estimated using the maximum likelihood approach. The performance of this estimation method is assessed via a simulation study. The flexibility of the DsPA distribution is shown using three count datasets. The DsPA distribution provides a better fit than some recent discrete models such as the discrete Burr-Ⅻ, uniform Poisson–Ailamujia, Poisson, discrete-Pareto, discrete-Rayleigh, discrete inverse-Rayleigh, and discrete Burr–Hutke distributions.