An innovative trigonometric technique for producing a new range of distributions: Implementations in the medical fields

Introducing new families of statistical distributions for data modeling in the medical sector is a fascinating area of research. Numerous methods have been developed and implemented for such purposes. Many of these methods rely on one or more additional parameters. However, the inclusion of new parameters can lead to certain consequences, such as re-parametrization problems. This paper also presents a novel family of distributions for generating statistical models. The proposed family is based on a trigonometric function and can be referred to as the weighted tangent family of distributions. A notable feature of the weighted tangent family is that it does not require any extra parameters. The paper also derives some mathematical properties and point estimators of the weighted tangent family. Furthermore, the paper focuses on a specific case within the weighted tangent family, namely the weighted tangent Weibull distribution. Finally, the paper considers three applications from the medical sector to demonstrate the effectiveness of the weighted tangent Weibull distribution. The practical illustrations underscore that the weighted tangent approach significantly improves the fitting capacity of the traditional models.