New classes of tests for the Weibull distribution using Stein's method in the presence of random right censoring

We develop two new classes of tests for the Weibull distribution based on Stein's method. The proposed tests are applied in the full sample case as well as in the framework of random right censoring. We investigate the finite sample performance of the new tests using a comprehensive Monte Carlo study. In both the absence and presence of censoring, it is found that the newly proposed classes of tests outperform competing tests against the majority of the distributions considered. In the cases where censoring is present we consider various censoring distributions. Some remarks on the asymptotic properties of the proposed tests are included. The paper presents another result of independent interest; the test initially proposed in Krit (2014) for use with full samples is amended to allow for testing for the Weibull distribution in the presence of censoring. The techniques developed in the paper are illustrated using two practical examples. In the first, we consider the survival times of patients with a certain type of leukemia. The second example is concerned with the initial remission times of leukemia patients, where the observed remission times are subject to random right censoring. We further include some concluding remarks along with avenues for future research.