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.

A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

“…where α and θ are the shape parameters while λ is the scale parameter. It is observed that F(x; α, λ, 1) reduces to the MAPTE by [18], F(x; → 1, λ, 1) tends to the exponential distribution, F(x; → 1, λ, 2) tends to the Rayleigh distribution, F(x; α, λ, 2) tends to the MAPT Rayleigh distribution and F(x; → 1, λ, θ) tends to the Weibull distribution. It is to mentioned hare that the MAPTW distribution can be considered as a weighted version of the APW distribution with weight function 1 + α − α 1−e −λx θ −2 .…”

“…For example, alpha power Weibull distribution by [8], alpha power generalized exponential by [15], alpha power transformed inverse Lindley distribution by [16] and alpha power Gompertz distribution by [17]. To add more flexibility to the APT method, Alotaibi et al [18] proposed a new form of the APT method which is called the modified APT (MAPT) method. The CDF and the PDF of the MAPT method are, respectively, given by…”

“…where α is a shape parameter, G(x) is a baseline distribution and g (x) = Ǵ (x). Reference [18] investigated the major properties of the new generator. They also used the new method to develop a new version of the exponential distribution and studied some of its properties.…”

A New Three-Parameter Inverse Weibull Distribution with Medical and燛ngineering Applications

“…See Johnson et al [17] for further information on the IW distribution. In this study, we offer a new three-parameter IW distribution utilizing the same idea proposed by Alotaibi et al [18]. The modified alpha power transformed IW (MAPTIW) distribution is the name given to the new distribution.…”

“…It includes some lifetime distributions, such as IW, inverted exponential and inverse Rayleigh distributions. Recently, The alpha power transformation approach was used by Alotaibi et al [18] to suggest a new method for adding a new shape parameter to a baseline distribution. Modified alpha power transformation (MAPT) was the name given to the approach they proposed.…”