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

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.

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

“…In the most recent times, attention towards the generalization of probability distributions has grown phenomenally high. For more insight, see the trustworthy work of Cordeiro and Brito [7], Zaka and Akhter [8], Al Mutairi et al [9], Tahir et al [10], Shahzad et al [11], Ahsan-ul-Haq et al [12], Okorie et al [13], Abdul-Moniem [14], Hassan et al [15], Zaka et al [16], Arshad et al [17], Arshad et al [18,19], Al-Mutairi [20], Alzaatreh et al [21], Gleaton and Lynch [22], Bourguignon et al [23], Afify et al [24], Tahir et al [25], Aldahlan et al [26], Aslam et al [27], Balogun et al [28], Afify et al [29], Mansour et al [30], Mahdavi and Kundu [31], Nassar et al [32], Ijaz et al [33], Klakattawi and Aljuhani [34], Afify et al [35], Alsubie et al [36], Ahmad et al [37], and Nofal et al [38].…”

A New Generalization of the Exponentiated Fréchet Distribution with Applications

“…This technique adds an extra parameter, α, to base distribution, making the resulting distribution more flexible in real-life modeling data with different failure rates. Several authors employed APT to propose new distributions such as the APT-Weibull by [32], APT-inverse Lindley by [14], APT-Pareto by [20], APT-Marshall-Olkin by [33], APT-Fréchet (APF) by [31], APT-Weibull Fréchet by [15], APT-inverse Lomax by [42], APT-Gompertz by [16], APT-exponentiated Weibull-exponential by [22] and APT-Weibull-exponential by [7], among others. The cumulative distribution function (CDF) and probability density function (PDF) of an APT are defined as:…”

New Method for Generating New Families of Distributions

“…Various studies have used this technique to introduce new distributions. These include the studies of [11], where the APT method was applied to the exponential distribution, [12], who presented the APT-Weibull distribution, [13] introduced the APT-Pareto distribution, [14] proposed the APT-inverse Lindley distribution, [15], introduced the APT-log logistic distribution, and [16] have recently proposed the alpha power exponentiated Weibull-exponential distribution.…”