Tan-G class of trigonometric distributions and its applications

In this paper, we introduce a new general class of trigonometric distributions based on the tangent function, called the Tan-G class. A mathematical procedure of the Tan-G class is carried out, including expansions for the probability density function, moments, central moments and Renyi entropy. The estimates are acquired in a non-closed form by the maximum likelihood estimation method. Then, an emphasis is put on a particular member of this class defined with the Burr XII distribution as baseline, called the Tan-BXII distribution. The inferential properties of the Tan-BXII model are investigated. Finally, the Tan-BXII model is applied to a practical data set, illustrating the interest of the Tan-G class for the practitioner.

Automated summary

This paper introduces a new general class of trigonometric distributions based on the tangent function, called the Tan-G class. The mathematical procedure and parameter estimation method were carried out for the Tan-G class, with a focus on the particular member Tan-BXII distribution. The application of the Tan-BXII model to a practical dataset illustrated the importance of the Tan-G class for practitioners.