Inverse Rayleigh–Exponentiated Weibull Distribution With a [0,1]-Truncated Generator: Properties and Applications

In this study, we introduce the inverse Rayleigh–exponentiated Weibull distribution with a [0, 1]-truncated generator, denoted by [0, 1] TIR–EW, as a novel member of the T–X family of distributions. Here, the notation [0, 1] refers to the truncation interval of the generator distribution and does not imply that the final random variable is supported on [0, 1]. Since the exponentiated Weibull distribution is used as the baseline, the proposed model is defined on the positive real line. The construction of the model is achieved by employing the inverse Rayleigh distribution as a generator and applying a [0, 1] truncation to the generator component within the T–X framework. We derive explicit analytical expressions for several fundamental statistical properties of the proposed distribution, including the cumulative distribution function, probability density function, survival and hazard rate functions, quantile function, probability-weighted moments, stress–strength reliability, and order statistics. To estimate the model parameters, a variety of classical and Bayesian estimation procedures are considered, and their finite-sample performance is assessed through an extensive Monte Carlo simulation study conducted in R. The practical utility and flexibility of the proposed model are further demonstrated through applications to positive real-valued lifetime and environmental datasets. The overall findings indicate that the [0, 1] TIR–EW distribution provides a highly adaptable and effective framework for modeling positive real-valued data with different distributional shapes and reliability characteristics.