A General Weighted Exponentiated Family of Distributions with Application to Carbon Fiber and Petroleum Rock Data

On the basis of power and exponential transformations, an original family of distributions is created and studied. Thanks to two tuning parameters, it has the capacity to generalize a few of the present families, which have been widely used in recent data. As a first contribution of this paper, a theoretical result is demonstrated on the admissible values of these parameters. Then, some of the properties of the family are established, including functional series expansions, quantile function, and moments. After that, we exemplify the theory; a special case based on the Weibull distribution is emphasized. It can be described as a new two-parameter lifetime distribution. It is of interest because of its original and flexible functionalities in terms of probability density and hazard rate shapes, and manageable properties, including a closed form expression of the quantile function. Five different and efficient estimation methods are examined for the point estimation of the parameters of this special distribution. A simulation work is performed to compare these estimation methods. Finally, we apply the special distribution to two real-world datasets to illustrate its usefulness, and compare it to some competitors, including some based on the Weibull distribution. According to the data analysis, the proposed distribution works well.