Development and Applications of a New Hybrid Weibull-Inverse Weibull Distribution

Abstract

This study introduces and applies a novel statistical model known as the hybrid Weibull inverse Weibull (HWIW) distribution, which combines the characteristics of the Weibull and inverse Weibull distributions to provide a more flexible model for representing real-world data, especially those characterized by asymmetry or extreme values. The basic functions of the distribution were derived, along with other statistical measures such as moments, the quantile function, and entropy were also derived. The distribution parameters were estimated using three distinct approaches, and their performance was evaluated through a Monte Carlo simulation to assess the performance and precision of each estimation technique. The results were used to show the most accurate estimation method for different samples. The proposed model was utilized to test two practical datasets; the findings demonstrated that the HWIW distribution outperformed six competing IW distributions in terms of model selection metrics. These results confirm the efficiency of the HWIW model’s ability to capture the structure of complex datasets and open the way for its use in multiple applications, including medical, industrial, and social fields, with the potential to be expanded to include multidimensional data or integrated with artificial intelligence techniques.