Generalized chi-squared based goodness-of-fit tests under progressive Type-II censoring for exponential and Weibull distributions

We propose new goodness-of-fit tests for exponentiality based on progressively Type-II censored data. These tests utilize scale-invariant statistics obtained from the Mahalanobis norm of normalized order statistics, leading to three test statistics, corresponding to L2-, L1-, and L∞-norms of centered uniform spacings. Exact and asymptotic distributions of these statistics are presented. A power study evaluates the proposed tests against existing benchmarks across various alternative distributions and censoring plans, demonstrating superior performance in cases with small and moderate sample sizes. Furthermore, we extend the methodology to approximate goodness-of-fit tests for Weibull distributions via power transformation, ensuring robustness w.r.t. the approximated significance level under unknown shape parameters. An illustrative data example confirms the practical applicability of our tests. Our findings highlight the potential for further extending goodness-of-fit tests under progressive Type-II censoring to other null distributions.