The Sine Alpha Power-G Family of Distributions: Characterizations, Regression Modeling, and Applications

This study develops a new method for generating families of distributions based on the alpha power transformation and the trigonometric function, which enables enormous versatility in the resulting sub-models and enhances the ability to more accurately characterize tail shapes. This proposed family of distributions is characterized by a single parameter, which exhibits considerable flexibility in capturing asymmetric datasets, making it a valuable alternative to some families of distributions that require additional parameters to achieve similar levels of flexibility. The sine alpha power generated family is introduced using the proposed method, and some of its members and properties are discussed. A particular member, the sine alpha power-Weibull (SAP-W), is investigated in depth. Graphical representations of the new distribution display monotone and non-monotone forms, whereas the hazard rate function takes a reversed J shape, J shape, bathtub, increasing, and decreasing shapes. Various characteristics of SAP-W distribution are derived, including moments, rényi entropies, and order statistics. Parameters of SAP-W are estimated using the maximum likelihood technique, and the effectiveness of these estimators is examined via Monte Carlo simulations. The superiority and potentiality of the proposed approach are demonstrated by analyzing three real-life engineering applications. The SAP-W outperforms several competing models, showing its flexibility. Additionally, a novel-log location-scale regression model is presented using SAP-W. The regression model’s significance is illustrated through its application to real data.