A new trigonometric-oriented distributional method: Model, theory, and practical applications - Omalsad Hamood Odhah; Olayan Albalawi; Huda M. Alshanbari (Alexandria Engineering Journal)
In this study, a new family of distributions is proposed, which incorporates a trigonometric function and is termed the weighted tan-G family. In comparison to various alternative methods, a key advantage of the proposed approach is its lack of requirement for additional parameters. The research includes a thorough examination of numerous mathematical properties related to the weighted tan-G family. For demonstration purposes, a particular model from this family, called the weighted tan-Weibull distribution, is investigated. The Weibull model serves as the foundational framework for this specific variant. The maximum likelihood estimators for the parameters of the weighted tan-Weibull distribution are obtained. A concise simulation study is conducted to assess these estimators. Furthermore, two applications from distinct sectors are examined to illustrate the practicality of the weighted tan-Weibull distribution. The first application demonstrates the survival times of patients diagnosed with a certain medical condition, while the second application, sourced from the hydrological sector, represents the highest points of flood events. Utilizing various decision-making tools, the weighted tan-Weibull distribution exhibits enhanced performance, surpassing other established variants of the Weibull distribution.