New inverse power type II Topp–Leone half-logistic distribution with applications in reliability and medical data

Modeling complex lifetime data requires statistical distributions that can capture skewness, heavy tails, and non-monotonic hazard behaviors. Classical models often provide a poor fit when applied to real data with such features. This study introduces a new model, the inverse power type II Topp–Leone half-logistic distribution, developed using the inverse transformation technique. The proposed distribution has a unimodal and right-skewed density, while its hazard function follows an upside-down bathtub shape, making it suitable for diverse survival and reliability studies. Several mathematical properties are derived, including the survival and hazard functions, quantile function, moments, inverse moments, and the moment generating function. Parameters are estimated using fifteen classical estimation methods, and a simulation study confirms the reliability and consistency of these estimators. To demonstrate practical relevance, the model is applied to three real-life datasets: active repair times of an airborne communication transceiver, times between successive airplane failures, and earthquake entrapment times. The proposed distribution outperforms well-known competing distributions in terms of the Akaike information criterion, Bayesian information criterion, consistent Akaike information criterion, and Hannan–Quinn information criterion, as well as the Anderson–Darling, Cramér–von Mises, and Kolmogorov–Smirnov test statistics. These findings underscore the practical relevance and versatility of the new model, particularly in applications such as reliability engineering, medical survival analysis, and risk assessment of natural disasters.