A new statistical approach with simulation study: Its implementations in management sciences and reliability

The analysis of practical phenomena is fundamentally reliant on probability distributions. This awareness has inspired researchers to develop new statistical models, resulting in a range of methodologies. Many of these methodologies are typically established with new parameters. Unfortunately, the addition of extra parameters can occasionally lead to complications concerning re-parameterization. Within this specific research domain, we propose a new statistical methodology intended to augment the distributional flexibility of probability models while avoiding the need for new parameters. This methodology, which merges the cosine function with the weighted T-X strategy, is designated as the cosine weighted-G (CW-G) family. We focus on the cosine weighted-Weibull (CW-Weibull) distribution, obtained through the CW-G method. Certain fundamental distributional functions pertaining to the CW-Weibull distribution are outlined, accompanied by visual depictions. We derive the quartile-based properties and formulates the maximum likelihood estimators. Additionally, a simulation study is performed to validate the theoretical findings. The relevance of the CW-Weibull distribution is affirmed through the scrutiny of two real-world data sets sourced from management sciences and reliability sectors. Our findings, derived from specific evaluation tests, indicate that the CW-Weibull distribution achieves optimal performance in the analysis of these data sets.