Statistical inference on the exponentiated moment exponential distribution and its discretization

Hasnain and Ahmad (2013) propose a two-parameter Exponentiated Moment Exponential (EME) Distribution and investigate its some characteristics. In this paper we study its additional properties in the context of its applications. The study classifies the EME distribution to homogeneous subfamilies with respect to hazard rate. A simulation study is conducted for EME distribution to observe the parameters for maximum likelihood and quartile estimates based on bias and mean square error. Based on EME distribution, we develop a discretized model that gives its importance in the industry. However, some important structural properties are studied for discrete Exponentiated moment exponential distribution with useful characterizations. Shapes of density and failure rate function of new discrete model are studied. Moreover, we provide justifications for the usefulness of the model and its enhanced scope as compared to the existing discretized model with the help of real-life data sets.