A Novel Gompertz-Type Distribution with Applications to Radiological Dose and Pharmacokinetic Data

This study introduces a novel four-parameter lifetime distribution constructed within the Topp–Leone Power Gompertz framework. Owing to its flexible structure, the proposed model accommodates a wide range of density shapes and hazard-rate patterns, including increasing, decreasing, bathtub-shaped, unimodal, and other non-monotone behaviors. Key distributional properties, including moments, entropy-based measures, quantile-based measures, and order statistics, are derived. Parameter inference is conducted using both likelihood-based and Bayesian approaches, and the finite-sample performance of the resulting estimators is assessed via Monte Carlo simulations. The practical relevance of the proposed distribution is illustrated using two real datasets and benchmarked against several competing lifetime models, including the Gompertz, Power Gompertz, Weibull, Topp–Leone Gompertz, Marshall–Olkin Gompertz, and Exponentiated Gompertz distributions. Overall, the comparative analyses demonstrate the superior fitting performance of the proposed model, highlighting its effectiveness for complex reliability, survival, and pharmacokinetic data.