THE PARALOGISTIC-CHEN DISTRIBUTION: A SUBMODEL OF THE PARALOGISTIC-{-} FAMILY, PROPERTIES AND APPLICATIONS

Analysis of lifetime data is fundamental in reliability and survival studies, yet classical distributions often fail to capture complex failure-rate patterns. To address this, we introduce the Paralogistic-Chen (PCh) distribution, a new lifetime model generated via the Transformed-Transformer (T-X) method, using the Paralogistic family as a generator and the Chen distribution as a baseline. Key mathematical properties are derived and a comprehensive Monte Carlo simulation study evaluates the finite-sample and asymptotic performance of the estimators, confirming their accuracy, stability, and convergence. Parameters are estimated using maximum likelihood estimation (MLE). Applications to real datasets, along with comparisons to existing models, demonstrate that the PCh distribution provides superior goodness-of-fit and flexibility in modeling diverse lifetime behaviors. Overall, the PCh distribution offers a versatile and robust alternative for reliability and survival analysis.