A New Class of the Power Function Distribution: Theory and Inference with an Application to Engineering Data

In this study, a new class that generates optimal univariate models called a new exponentiated-G class of distributions is developed. Numerous complementary statistical properties are derived and discussed in detail for the newly exponentiated power function (EPF) distribution. All possible shapes of the probability density and hazard rate functions are sketched for selected values of parameters. Six accredited estimation methods are discussed, and their performance is assessed and compared by a simulation study. The applicability of the new class is evaluated by analyzing the automotive engineering sector data.

Automated summary

In this study, a new class of distributions called the new exponentiated-G class is developed for generating optimal univariate models. Various statistical properties of the newly introduced exponentiated power function (EPF) distribution are derived and discussed. The applicability of this new class is evaluated by analyzing data from the automotive engineering sector.