A new trigonometric-oriented statistical distribution: Model, theory, and applications in physics and engineering sectors

Recent developments have led to the introduction of new probability distributions for data modeling in applied sciences. However, many of these models include extra parameters. The presence of these additional parameters gives rise to complications concerning estimation and re-parametrization. This paper proposes a new probability distribution without additional parameters, to address these issues. The proposed probability distribution is obtained by merging the Weibull distribution with a known trigonometric distributional method and is referred to as the modified arcsine-tangent Weibull distribution. Various statistical properties of the modified arcsine-tangent Weibull distribution are derived. The parameters associated with the modified arcsine-tangent Weibull distribution are estimated through the application of the maximum likelihood estimation method. A simulation study is also provided for the modified arcsine-tangent Weibull distribution to assess the performance of its estimators. The modified arcsine-tangent Weibull distribution is ultimately demonstrated through the analysis of two applications within the physics and engineering related sectors, with a particular emphasis on the breaking strength of carbon fibers. Through the use of four essential selection criteria, it becomes apparent that the modified arcsine-tangent Weibull distribution is the preeminent model in competition for the breaking strength of carbon fiber data sets.