A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family

Wedad H. Aljuhani,Hadeel S. Klakattawi

doi:10.3390/sym13030412

Abstract

In the following article, a new five-parameter distribution, the alpha power exponentiated Weibull-exponential distribution is proposed, based on a newly developed technique. It is of particular interest because the density of this distribution can take various symmetric and asymmetric possible shapes. Moreover, its related hazard function is tractable and showing a great diversity of asymmetrical shaped, including increasing, decreasing, near symmetrical, increasing-decreasing-increasing, increasing-constant-increasing, J-shaped, and reversed J-shaped. Some properties relating to the proposed distribution are provided. The inferential method of maximum likelihood is employed, in order to estimate the model’s unknown parameters, and these estimates are evaluated based on various simulation studies. Moreover, the usefulness of the model is investigated through its application to three real data sets. The results show that the proposed distribution can, in fact, better fit the data, when compared to other competing distributions.

Highlights

Various techniques for constructing families to generate new modified distributions that better fit applicable data sets have been suggested in the academic literature
The results show that the mean squared error (MSE) decreased as the sample size n increased
The five-parameter alpha power exponentiated Weibull-exponential distribution (APEWED) distribution was introduced, based on a new technique for generating distributions. This method combines two well-known families of distributions-namely, exponentiated T-X and alpha power transformation (APT)- in order to allow for more flexibility and adaptability in fitting practical data sets

Summary

Introduction

Various techniques for constructing families to generate new modified distributions that better fit applicable data sets have been suggested in the academic literature. [12] have suggested an innovative technique for introducing an additional parameter to a family of distributions. This new technique has been referred as the alpha power transformation (APT) family of distributions. This study combines two techniques-exponentiated T-X and APT-in order to develop a new five-parameter distribution, called the alpha power exponentiated Weibull-exponential distribution (APEWED). This rest of the article is organized as follows: Section 2 introduces the APEWED with some special cases along with its survival and hazard functions.

Some Special Cases of the APEWED

Graphical Presentations of the APEWED

Expansion of the PDF of the APEWED

Moments

Moment Generating Function and Characteristic Function

Mean Residual Life and Mean Waiting Time

Shannon and Rényi Entropies

Order Statistics

Maximum Likelihood Estimation

Simulation Study

Applications

Conclusions