Robust explicit estimators of the Rayleigh distribution under Type II censoring

In this paper, we consider robust explicit estimators for the two-parameter Rayleigh distribution under Type II censoring, addressing challenges posed by data contamination. We propose two alternative estimation methods: M-estimation and power-weighted repeated medians (PWRM) as robust alternatives to conventional estimators derived from the maximum likelihood (ML) and ordinary least squares (OLS) approaches. We conduct simulation studies to investigate the efficiency and robustness of these estimators in clean and contaminated data sets. Numerical results show that while all methods perform comparably in the absence of data contamination, the PWRM estimator outperforms OLS and ML in contaminated cases in terms of achieving high relative efficiency and maintaining stability across different levels of censoring considered. Finally, we provide a real-data application for illustrative purposes. Our findings highlight the advantages of robust estimation techniques in improving the accuracy of parameter estimation for the analysis of data with potential data anomalies.