A new statistical model with Monte Carlo simulation: Theory and applications in music education and reliability engineering

Probability distributions are fundamental to the study of real-world phenomena, but there are occasionally very few practical ways to achieve peak performance. As a result of this fact, therefore, numerous researchers have started to pursue new statistical models. This study also proposes a novel statistical model called arcsine tangent flexible Weibull (ASTF-Weibull) distribution. The ASTF-Weibull distribution is the product of combining the flexible Weibull extension distribution with an established trigonometric distributional method. Certain distributional properties, particularly those related to quartiles, are derived for the ASTF-Weibull distribution. The maximum likelihood estimation method is employed to obtain the estimators for the parameters of the ASTF-Weibull distribution. In addition, a simulation study is performed to evaluate the reliability of these estimators. Finally, we conduct a practical exploration of the practicality of the ASTF-Weibull distribution by analyzing two different data sets. Music education is the subject of the first data set, while reliability engineering is the subject of the second data set. Our empirical study provides convincing evidence that the ASTF-Weibull distribution is suitable for modeling both data sets. When comparing the ASTF-Weibull distribution with the conventional and unconventional probability distributions, it is clear that the ASTF-Weibull distribution is superior.