On a Comparative Study on Some Trigonometric Classes of Distributions by the Analysis of Practical Data Sets

Abstract

The aim of this paper is twofold. Firstly, we elaborate and investigate a new trigonometric class of distribution, called the type II Tan-G class. Secondly, we perform a practical comparative evaluation of certain trigonometric classes; the Sin-G, Cos-G, Tan-G classes and the new one, with each other and with their common baseline distribution. More specifically, the usefulness and flexibility of these trigonometric classes are demonstrated through twelve practical data sets, by using the Weibull distribution as baseline. Among the data sets, two of them concern the Covid-19 pandemic in France from March to June 2020. As main results, it is shown that the related trigonometric models can outperform the former Weibull model in various cases and that the proposed type II Tan Weibull model can be, in certain situations, the best of them. The main lines of the code written in the $\textsf{R}$ software language are provided.