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

Abstract

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 presence 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. We present another result of independent interest; a test initially proposed 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.

On a new class of tests for the Pareto distribution using Fourier methods

“…Some work in this regard has been done by Fernández and Rivera (2020), where they consider Kaplan‐Meier $$$ U $$$ and $$$ V $$$ statistics, and by Cuparić and Milošević (2022), where they derive asymptotic results for a new characterization based test for exponentiality in the presence of random right censored data. Further details regarding the development of tests for the censored exponential distribution can be found in Bothma et al (2021), while Bothma et al (2022) consider tests for the censored Weibull distribution. For results pertaining specifically to tests for the censored Pareto distribution, the interested reader is referred to Ndwandwe et al (2021).…”