Efficient Estimation Methods for the QR Distribution with Type-II Censored Data: An Empirical Validation on Lung Cancer Prognosis

The QR distribution, recently introduced for modeling lifetime data under Type-II censoring, offers a flexible framework for survival and reliability analysis. This study provides the first comprehensive evaluation of multiple modern estimation techniques for the QR distribution under Type-II censoring. We systematically compare classical maximum likelihood estimation with stochastic gradient descent variants (Momentum and Adam), Bayesian approaches including Maximum A Posteriori estimation, Markov Chain Monte Carlo, and Variational Inference, as well as machine learning-integrated methods such as amortized neural network inference. Using both synthetic and the real Veterans’ Administration Lung Cancer dataset, we evaluate these methods in terms of parameter estimation accuracy, computational efficiency, and convergence behavior. The results demonstrate the strengths of optimization-based, Bayesian, and neural approaches, highlighting their practical utility in handling complex censored survival data. This research validates the distribution’s effectiveness in capturing survival dynamics, offering valuable insights for clinical applications and highlighting areas for methodological improvement.