Document Type : Original Article
Authors
1
Department of Basic Sciences, Higher Institute for Administrative Sciences and Foreign Trade, Cairo, Egypt
2
Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
3
Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt
4
Department of Basic Sciences, Al Madina Higher Institute of Management and Technology, Giza, Egypt
Abstract
The goal of this work is to create an innovative heavy-tailed distribution known as the arctan-Kumaraswamy exponential (ATKE) distribution. The Kumaraswamy exponential distribution and the arctan-X family of distributions were combined to create the ATKE distribution. The ATKE distribution is adaptable and capable of modeling a range of hazard rate shapes when compared to the conventional Kumaraswamy exponential distribution. Different asymmetric and unimodal forms are seen in the densities. The many types of decreasing, rising, increasing-constant, and reversed j-shaped shapes are depicted by the hazard rate functions. The created model is evaluated from a statistical viewpoint. Various metrics of uncertainty are calculated. Six commonly applied statistical techniques are employed, in the field of research, to estimate the parameters of the distribution. To illustrate the effectiveness of the maximum likelihood, Cramer-von Mises, least squares, Anderson-Darling (AD), weighted least squares, and the right-tail AD estimators of the ATKE distribution parameters, we conducted an extensive simulation analysis. Additionally, the adaptability of the provided model was examined using a dataset of renewable energy sources, demonstrating that, in comparison to some other competing models that contain two, three and four parameters, the suggested model could potentially utilize to fit these data.
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