The Exponentiated Power Alpha Index Generalized Family of Distributions: Properties and Applications

Abstract

The study of hydrological characteristics has a vital role in designing, planning, and managing water resources. The selection of appropriate probability distributions and methods of estimations are basic elements in hydrology analyses. In this article, a new family named the ‘exponentiated power alpha index generalized’ (EPAIG)-G is proposed to develop several new distributions. Using this proposed family, we developed a new model, called the EPAIG-exponential (EPAIG-E). A few structural properties of the EPAIG-G were obtained. The EPAIG-E parameters were estimated through the method of maximum likelihood (MML). The study of the Monte Carlo simulation (MCS) was produced for the EPAIG-E. The model performance is illustrated using real data.

Keywords

• quantiles
• moments
• entropies
• likelihood
• exponentiated
• asymptotic