Beyond the Sin-G family: The transformed Sin-G family.

In recent years, the trigonometric families of continuous distributions have found a place of choice in the theory and practice of statistics, with the Sin-G family as leader. In this paper, we provide some contributions to the subject by introducing a flexible extension of the Sin-G family, called the transformed Sin-G family. It is constructed from a new polynomial-trigonometric function presenting a desirable "versatile concave/convex" property, among others. The modelling possibilities of the former Sin-G family are thus multiplied. This potential is also highlighted by a complete theoretical work, showing stochastic ordering results, studying the analytical properties of the main functions, deriving several kinds of moments, and discussing the reliability parameter as well. Then, the applied side of the proposed family is investigated, with numerical results and applications on the related models. In particular, the estimation of the unknown model parameters is performed through the use of the maximum likelihood method. Then, two real life data sets are analyzed by a new extended Weibull model derived to the considered trigonometric mechanism. We show that it performs the best among seven comparable models, illustrating the importance of the findings.