A new weighted version of alpha power transformation method: properties and applications to COVID-19 and software reliability data

Abstract

This paper is an effort to propose a new method to generate probability distributions based on alpha power transformation method for more flexibility. We refer to the new method as modified alpha power transformed method. The new proposed method can be considered as a weighted version of the alpha power transformation method with more ability to model various types of data. A special case has been studied in detail namely; one parameter exponential distribution. The new generalization of the traditional exponential distribution provides a better fit than the exponential distribution and some competitive models. It appears to be a distribution capable of allowing constant, decreasing and increasing hazard rates based on its parameters. Various properties of the new method as well as the new distribution are derived, including explicit expressions for the quantiles, moments, moment generating function and expression of entropies. The point and interval estimations are investigated using maximum likelihood method. A simulation study is carried out and two applications, one for COVID-19 data and the other for software reliability data are considered to show the flexibility of the proposed distribution. The results show that the new distribution provides a better fit than some other competitive distributions including exponential, alpha power exponential, Weibull and gamma distributions.