ABSTRACT In this study, a new class of probability distributions termed T‐Nadarajah‐Haghighi (T‐NHY) family, by generalizing the two‐parameter Nadarajah–Haghighi distribution through the T‐RY framework. The flexibility of the class is enhanced by incorporating quantile functions from several known distributions including, Uniform, Exponential, Weibull, Log‐Logistic, Logistic, and Cauchy, which yield six distinct subclasses. Several statistical properties of the proposed T‐NHY class, including quantile functions, hazard rates, entropy, and moments, are derived. Further, four specific member models within the proposed class have been explored in detail. Parameter estimation techniques including maximum likelihood estimation (MLE), Anderson‐Darling estimation (ADE), and the least squares estimation (LSE) methods are applied. The applicability and superiority of the proposed models are demonstrated using three real‐life applications; vinyl chloride concentrations, bladder cancer remission times, and breaking stress of carbon fibers. Comparative analysis based on model selection criteria (AIC, BIC, HQIC, etc. ) demonstrates that the T‐NHY family provides a better fit relative to traditional models, confirming its practical significance in modeling diverse lifetime and reliability data.
Hussain et al. (Mon,) studied this question.