A flexible statistical distribution for capturing complex patterns in industrial data

The effective modeling of real-world data requires flexible statistical distributions to accurately capture complex patterns. For that purpose, this paper introduces an extension of the XLindley distribution, specifically designed for modeling textile data. The suggested Marshall-Olkin transmuted XLindley distribution (MOTXLD) has additional shape and transmuted parameters, which considerably influence its skewness, kurtosis, and tail behavior. The MOTXLD is versatile and can have right-skewed, uni-modal, or reversed-J-shaped density curves. A comprehensive statistical analysis of the MOTXLD is conducted, including the derivation of key properties. To estimate the model parameters, both frequentist and Bayesian techniques are implemented. The bootstrap approach, the normal approximation method, and Bayesian credible intervals are some of the techniques employed to build confidence intervals. A simulation study is conducted to assess the efficiency of the estimated parameters. According to the outcomes of this study, Bayesian estimates often perform better than frequentist estimates. Bayesian credible intervals generally show a higher coverage probability compared to confidence intervals based on maximum likelihood estimation, implying more reliable interval estimates. The adaptability of the proposed distribution is demonstrated using real datasets from the textile industry sector, highlighting its potential for effective modeling in this domain.