A new trigonometric-based statistical model: Its empirical implementations in music education and reliability engineering

Abstract

The impact of statistical distributions in effectively representing practical scenarios and supporting informed decision-making is well acknowledged across various fields. However, it is crucial to recognize that the limitations of these distributions can occasionally impede optimal fitting in certain situations. This awareness has prompted researchers to investigate improved and more efficient probability distributions. Based on empirical evidence, this paper introduces a novel probability distribution called the arcsine-tangent generalized inverse Weibull (ASTGI-Weibull) distribution. The new model is derived from the combination of the generalized inverse Weibull distribution and a probabilistic approach inspired by the arcsine-tangent concept. Specific statistical properties, particularly those associated with quantiles, have been derived for the ASTGI-Weibull distribution. An established method of estimation is used to calculate the point estimators for this distribution, followed by the conduction of a simulation study. This study also investigates two data sets, one related to music education and the other to reliability engineering, to showcase the practical benefits of the ASTGI-Weibull distribution. The empirical fitting of the ASTGI-Weibull distribution is compared with several other distributions, employing the given data sets for comparative analysis. The findings demonstrate that the ASTGI-Weibull distribution is the most effective among the various distributions considered.