A New Weibull–Rayleigh Distribution: Characterization, Estimation Methods, and Applications with Change Point Analysis

Many scholars are interested in modeling complex data in an effort to create novel probability distributions. This article proposes a novel class of distributions based on the inverse of the exponentiated Weibull hazard rate function. A particular member of this class, the Weibull–Rayleigh distribution (WR), is presented with focus. The WR features diverse probability density functions, including symmetric, right-skewed, left-skewed, and the inverse J-shaped distribution which is flexible in modeling lifetime and systems data. Several significant statistical features of the suggested WR are examined, covering the quantile, moments, characteristic function, probability weighted moment, order statistics, and entropy measures. The model accuracy was verified through Monte Carlo simulations of five different statistical estimation methods. The significance of WR is demonstrated with three real-world data sets, revealing a higher goodness of fit compared to other competing models. Additionally, the change point for the WR model is illustrated using the modified information criterion (MIC) to identify changes in the structures of these data. The MIC and curve analysis captured a potential change point, supporting and proving the effectiveness of WR distribution in describing transitions.