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

• Main Authors: Hadeel S. Klakattawi, Wedad H. Aljuhani
• Format: Article
• Language: English
• Published: MDPI AG 2021-03-01
• Series: Symmetry
• Subjects: alpha power transformation; exponentiated T-X family; Weibull distribution; exponential distribution; maximum likelihood estimation
• Online Access: https://www.mdpi.com/2073-8994/13/3/412

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.