The choice of probability distribution is strongly data-dependent, as observed in several studies. Given the central role of statistical distribution in predictive analytics, researchers have continued to develop new models that accurately capture underlying data behaviours. This study proposes the Hybrid Weibull–Exponentiated Rayleigh distribution developed by compounding the Weibull and Exponentiated Rayleigh distributions via the T-X transformation framework. The new three-parameter distribution is formulated to provide a flexible modelling framework capable of handling data exhibiting non-monotone failure rates. The properties of the proposed distribution, such as the cumulative distribution function, probability density function, survival function, hazard function, linear representation, moments, and entropy, are studied. We estimate the parameters of the distribution using the Maximum Likelihood Estimation technique. Furthermore, the impact of the proposed distribution parameters on the distribution’s shape is studied, particularly its symmetry properties. The shape of the distribution varies with its parameter values, thereby enabling it to model diverse data patterns. This flexibility makes it especially useful for describing the presence or absence of symmetry in real-world failure processes. Simulation studies are conducted to assess the behaviour of the estimators under different parameter settings. The proposed distribution is applied to real-world data to demonstrate its performance. Comparative analysis is performed against other well-established models. The results indicate that the proposed distribution outperforms other models in terms of goodness-of-fit, demonstrating its potential as a superior alternative for modelling lifetime data and reliability analysis based on Akaike Information Criterion and Bayesian Information Criterion.
Adeniji et al. (2026) studied this question.