Discriminating Between Weibull and Log‐Normal Distributions in the Presence of Hybrid Censoring

The Weibull and lognormal distributions are two of the most widely used models for analyzing lifetime data. Both share several properties, and for certain parameter ranges, their cumulative distribution functions can appear quite similar. However, choosing the more suitable distribution is essential for accurate inference. When data are subject to censoring, the problem becomes more complex. Here, we assume that the data come either from a Weibull or a lognormal distribution under hybrid censoring (considering both Type‐I and Type‐II hybrid schemes). To discriminate between the two models, we use the ratio (or equivalently, the difference) of their maximized log‐likelihoods (RML). We further employ a recently developed method based on minimum density power divergence estimators (MDPDE) and compare its performance with the classical likelihood approach in both without outliers and with outliers settings, where it shows clear superiority. In addition, a Bayesian decision criterion is implemented and compared with these methods. The asymptotic distribution of the RML statistic is derived to compute the probability of correct selection and to determine the minimum required sample size for reliable discrimination. Simulation studies are carried out to evaluate how well the asymptotic results hold across different sample sizes, censoring levels, and censoring times. The asymptotic approximations perform well even for moderate sample sizes. Finally, we investigate the effect of model misspecification on key reliability measures, including the th quantile, mean residual life, reliability function, and prediction for future failures. A real data set is analyzed to illustrate the proposed methods.