Inverse Weibull-Rayleigh Distribution with Properties and Applications: A Member of the Inverse Weibull-X Family

Abstract

This research introduces a novel class of distributions termed the inverse Weibull-X (IW-X) family, derived from the broader T-X family of distributions. We systematically develop and describe several expanded sub-models within this newly proposed family, focusing on their unique characteristics and advantages. A particular emphasis is placed on the extended model known as the Inverse Weibull-Rayleigh (IW-R) distribution. This model is explored in depth, detailing its distributional properties, inferential methods, and practical applications. We provide a comprehensive theoretical framework for the IW-R distribution, including derivations of its moments, reliability functions, and other key statistical properties. Additionally, we discuss estimation techniques for the model parameters, utilizing the maximum likelihood estimation. The practical utility of the IW-R distribution is demonstrated through application to real-life data sets. These examples illustrate the model's enhanced adaptability and robustness in fitting data across various domains. The results indicate that the IW-R distribution offers significant improvements in flexibility and accuracy over traditional models, highlighting its potential as a valuable tool for statistical analysis and inference in diverse applications.