Modeling engineering and medical lifetime data using a flexible extension of the XShanker distribution under censoring

The complexity of today's lifetime data necessitates more adaptable probability models. To address this need, we develop the Cosine Topp-Leone XShanker Distribution (CTL-XSD), a novel two-parameter extension of the XShanker distribution. We provide the mathematical properties of the new model, including its moments, incomplete moments, identifiability, quantiles, Lorenz curve, and Bonferroni curve. Using Type-II censoring, we employ both classical and Bayesian methods to estimate the parameters, survival function, and hazard function. Using Markov Chain Monte Carlo techniques, we derive Bayesian point and credible interval estimates under both symmetric and asymmetric loss functions. Additionally, we obtain the asymptotic confidence intervals based on the Fisher information matrix. We also provide a numerical study to evaluate the performance of the various estimators. We compare our findings with those from other models in the context of lifetime data analysis. The CTL-XSD outperformed the alternative models in terms of the Kolmogorov-Smirnov test statistic, with values of 0.98886 and 0.98438 in the context of engineering and medical datasets, respectively, with the lowest values in terms of all information criteria.