A new weighted flexible Weibull model with parameter estimation: Its applications to dance education and radiation sector

Accurately modeling the real-world events having mixed failure rates or dealing with large losses (or extreme value phenomena) cannot be achieved through the implementation of the Weibull distribution or other conventional distributions. To accurately address these facts, this paper considers the development, assessment, and implementation of a new probability distribution. We develop the proposed new weighted flexible Weibull (NWF-Weibull) distribution by merging the flexible Weibull extension distribution with a known distributional method called a new modified exponential- X method. For the NWF-Weibull distribution, certain mathematical properties including the quantile-oriented properties and heavy-tailed characteristic are established. The mathematical formulation of the point estimators for the NWF-Weibull distribution is acquired. Furthermore, a simulation study is carried out using different parameter combinations of the NWF-Weibull distribution to evaluate the performance of the estimators. Ultimately, the practical assessment of the NWF-Weibull distribution is conducted using two practical data sets pertaining to dance education and radiation sciences. The empirical findings, based on four established criteria, indicate that the NWF-Weibull distribution exhibits superiority over several existing probability distributions.