A Sequential Design for Extreme Quantile Estimation Under Binary Sampling
Year: 2026
Type: article
Abstract: We propose a sequential design method aiming at the estimation of an extreme quantile based on a sample of binary data corresponding to peaks over a given threshold. This study is motivated by an industrial challenge in material reliability and consists of estimating a failure quantile from trials whose outcomes are reduced to indicators of whether the specimen has failed at the tested stress levels. The proposed approach relies on a splitting strategy that decomposes the target extreme probability into a product of higher-order conditional probabilities, enabling a progressive exploration of the tail of the distribution through sampling under truncated laws. We consider GEV and Weibull models for the underlying distribution, and the sequential estimation of their parameters is carried out using an enhanced maximum likelihood procedure specifically adapted to binary data, addressing the substantial uncertainty inherent to such limited information.
Source: Entropy
DOI: 10.3390/e28040479
Authors: Michel Broniatowski, Emilie Miranda
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7155203722
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