An innovative statistical framework: A simulation study and practical implementations in the dance education, reliability engineering and radiation sector

This novel research effort aims to contribute to the literature on probabilistic-oriented methods for illustrating real-world events within different sectors. The new work is based on developing a new distribution family, referred to as the inverted sine Zubair- G (ISZ- G ) family. The ISZ- G family is composed of merging the flexibility of the Zubair- G method with the inverse trigonometric-based method. To illustrate the ISZ- G in the practical scenarios, we consider the Weibull distribution as its special case, referred to as the inverted sine Zubair–Weibull (ISZ-Weibull) distribution. The mathematical computation of the quantile function of the ISZ-Weibull distribution is carried which are further utilized to compute other mathematical properties. The computation of the point estimators along with the simulation studies are presented. Besides the theoretical work, we also consider the practical implications of the ISZ-Weibull distribution within numerous applied fields such as dance education, reliability engineering and the radiation sector. This is done with the intention to prove the superiority of the ISZ-Weibull distribution over some existing distributions. Based on numerous statistical outlets, we observe that the ISZ-Weibull distribution is a more powerful outlet than certain rival tools available in the literature.