Weibull distribution, Sine function, Quartile function, Management sciences, Reliability sector, Statistical modeling, Engineering (General). Civil engineering (General), TA1-2040

The study of real-world phenomena fundamentally hinges on probability distributions. This understanding has inspired researchers to design new statistical models, which has resulted in a variety of methodologies. Often, these methodologies are developed with new parameters. Unfortunately, the introduction of additional parameters can sometimes create difficulties related to re-parameterization. In the context of this particular research area, we introduce a groundbreaking statistical methodology designed to enhance the distributional flexibility of probability models without the addition of new parameters. The methodology we propose, which combines the sine function with the weighted T-X strategy, is referred to as the sine weighted-G (SW-G) family. The sine weighted-Weibull (SW-Weibull) distribution is examined through the SW-G method. Essential distributional functions for the SW-Weibull distribution are presented, along with corresponding visual representations. Additionally, properties based on quartiles are explored, and the derivation of maximum likelihood estimators is presented. A simulation study is conducted to enhance the understanding of the distribution. Ultimately, the relevance of the SW-Weibull distribution is confirmed by examining two real-world data sets from the management sciences and reliability sectors. Our findings, based on particular evaluation tests, indicate that the SW-Weibull distribution provides optimal performance when analyzing the aforementioned data sets.