New Arctan-generator family of distributions with an example of Frechet distribution: Simulation and analysis to strength of glass and carbon fiber data

Abstract

Since standard distributions do not fundamentally have an acceptable fit to all types of data sets, it is necessary to construct extensions of standard distributions to increase their capability in data modeling. As a result of this shortage in old ones, we proposed a novel generator based on the trigonometric function (Arctan). We selected the Frechet distribution as the baseline for the generator’s applicability. This generator produces the “new Arctan Frechet distribution” (NATFD). The fundamental properties of the proposed distribution have been taken into consideration. Estimating the given distribution’s parameters is accomplished using the maximum-likelihood method. A simulation study is carried out to evaluate the superiority of the proposed distribution, and two actual data sets are used.

Keywords

• Arctan
• Frechet distribution
• Moments
• Reliability study
• Maximum likelihood estimation