A new statistical distribution: Its empirical exploration using the reliability and lifespan data in fashion industry

The importance of statistical distributions in accurately representing real-world scenarios and aiding in informed decision-making is well recognized. Nevertheless, it is crucial to acknowledge that the limitations of these distributions can hinder optimal fitting in certain situations. This awareness has led researchers to investigate improved and more appropriate probability distributions. Grounded in factual motivation, this study proposes a new technique for generating updated iterations of current probability distributions. The technique is designated as the modified cosine- G (MC- G ) family. For demonstration purposes, the paper focuses on a particular model based on the Weibull distribution, specifically the modified cosine-Weibull (MC-Weibull) distribution. The derivation of specific statistical properties, especially those concerning quantiles, has been accomplished. A conventional estimation method is applied to ascertain the point estimators of the MC-Weibull distribution, and a simulation study is subsequently performed. To illustrate the benefits of the MC-Weibull distribution, two data sets from the reliability sector and the fashion industry are examined. The empirical fitting of the MC-Weibull distribution is compared against various alternative distributions, utilizing these data sets for the analysis. By applying specific benchmarks for assessment, it has been concluded that the MC-Weibull distribution achieves the best and most optimal fit for both data sets.