Inferential development and modelling of the cancer survival data with Lehmann type upper-bounded distribution

This paper introduces a Lehmann-type upper-bounded tau distribution as a flexible model for random variables with a finite upper endpoint. The main statistical properties of the proposed distribution are derived, including moments, skewness, kurtosis, and several quantile-based measures, while stochastic ordering with respect to the shape parameter is also investigated. The hazard rate function is studied in detail and is shown to accommodate increasing, decreasing, and bathtub failure-rate patterns, providing flexibility for lifetime and survival-time modelling. Classical and Bayesian inference procedures are developed for estimating the model parameters. A closed-form quantile function is obtained, which facilitates random variate generation and enables extensive Monte Carlo simulations to examine the finite-sample performance of the proposed estimators. The practical applicability of the proposed model is illustrated using real survival-time datasets, where the model provides a suitable representation of bounded survival distributions and allows the finite upper endpoint to be incorporated into the analysis. The proposed distribution therefore offers a mathematically tractable and flexible alternative to existing lifetime models when a finite upper limit is appropriate.