An exponential goodness-of-fit test for randomly censored data based on the hellinger divergence

This paper proposes a new goodness-of-fit test based on the Hellinger distance for assessing exponentiality under random censoring. The proposed statistic is constructed using the Vasicek estimator, and its asymptotic properties, including asymptotic normality and consistency, are established theoretically under the Koziol–Green censoring model. The performance of the test is evaluated through extensive Monte Carlo simulations and compared with competing tests, including Kolmogorov–Smirnov, Cramér–von Mises, Anderson–Darling, and information-based statistics. The results indicate that the proposed test generally performs competitively and exhibits higher power, particularly against heavy-tailed and skewed alternative distributions. The practical utility of the method is illustrated through the analysis of real data. The computed p-values for the proposed test and its competitors indicate that, at the 5% significance level, there is insufficient evidence to reject the exponential model for the considered data. These findings are consistent with previous studies and demonstrate the effectiveness of the proposed test in practical survival analysis applications.