Extreme value model under an adaptive progressive Type-II censoring: application of a pivotal quantity

다국어 초록 (Multilingual Abstract)

This study introduces a novel pivotal-based approach, specifically designed for an adaptive progressive Type-II censoring framework. As an illustrative example of the proposed methodology, we focus on an adaptive progressive Type-II censored sample from an extreme value distribution with location and scale parameters, which is useful for modeling the occurrence probabilities of extreme events such as natural disasters and financial crises. The proposed methodology not only offers very simple estimation equations for the two parameters but also constructs an exact confidence interval for the scale parameter, by utilizing pivotal quantities. Furthermore, it enables the construction of a generalized confidence interval for the location parameter, which may meet nominal levels even when the sample size is not sufficiently large. To facilitate this, an algorithm employing a pseudorandom sequence is proposed, which is attractive due to its outstanding scalability. This scalability is demonstrated through the construction of a generalized interval for an adaptive progressive Type-II censored sample. Finally, the superiority and practical applicability of the proposed methodology are validated through a comparison with a likelihood-based method in Monte Carlo simulations and real data analysis.