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Structure of hybrid censoring schemes and its implications

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  • Erhard Cramer

    (RWTH Aachen University)

Abstract

In this paper, structural properties of (progressive) hybrid censoring schemes are established by studying the possible data scenarios resulting from the hybrid censoring scheme. The results illustrate that the distributions of hybrid censored random variables can be immediately derived from the cases of Type-I and Type-II censored data. Furthermore, it turns out that results in likelihood and Bayesian inference are also obtained directly which explains the similarities present in the probabilistic and statistical analysis of these censoring schemes. The power of the approach is illustrated by applying the approach to the quite complex unified Type-II (progressive) hybrid censoring scheme. Finally, it is shown that the approach is not restricted to (progressively Type-II censored) order statistics and that it can be extended to almost any kind of ordered data.

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  • Erhard Cramer, 2025. "Structure of hybrid censoring schemes and its implications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(3), pages 393-417, April.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:3:d:10.1007_s00184-024-00960-6
    DOI: 10.1007/s00184-024-00960-6
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    References listed on IDEAS

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    1. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    2. Ping Chan & Hon Ng & Feng Su, 2015. "Exact likelihood inference for the two-parameter exponential distribution under Type-II progressively hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 747-770, August.
    3. Julian Górny & Erhard Cramer, 2018. "Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 173-210, February.
    4. Xiaojun Zhu & N. Balakrishnan & Helton Saulo, 2019. "On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 759-778, October.
    5. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
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