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Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring

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Abstract

In this paper, a structural analysis of hybrid censoring models is presented. This new modularization approach to hybrid censoring models enables a convenient derivation of distributional results. For instance, it allows to derive the exact distribution of the MLEs under an exponential assumption for very complex hybrid scenarios. In order to illustrate the benefit of this idea, we apply it to four new unified progressive hybrid censoring schemes. They are extensions of already proposed unified Type-I/II/III/IV hybrid censoring schemes to progressively Type-II censored data. The resulting analysis shows that the modularization approach provides a powerful, efficient, and elegant tool to study even more complex hybrid censoring models.

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References

  • Balakrishnan N, Cramer E (2014) The art of progressive censoring: applications to reliability and quality, statistics for industry and technology. Springer, New York

    Book  MATH  Google Scholar 

  • Balakrishnan N, Kundu D (2013) Hybrid censoring: models, inferential results and applications. Comput Stat Data Anal 57(1):166–209

    Article  MathSciNet  MATH  Google Scholar 

  • Balakrishnan N, Rasouli A, Farsipour NS (2008) Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution. J Stat Comput Simul 78(5):475–488

    Article  MathSciNet  MATH  Google Scholar 

  • Burkschat M, Cramer E, Górny J (2016) Type-I censored sequential \(k\)-out-of-\(n\) systems. Appl Math Model 40:8156–8174

    Article  MathSciNet  Google Scholar 

  • Chandrasekar B, Childs A, Balakrishnan N (2004) Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring. Naval Res Logist (NRL) 51(7):994–1004

    Article  MathSciNet  MATH  Google Scholar 

  • Childs A, Chandrasekar B, Balakrishnan N (2008) Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems, statistics for industry and technology. Birkhäuser, Boston, pp 323–334

    Google Scholar 

  • Childs A, Chandrasekar B, Balakrishnan N, Kundu D (2003) Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Ann Inst Stat Math 55(2):319–330

    MathSciNet  MATH  Google Scholar 

  • Cramer E, Balakrishnan N (2013) On some exact distributional results based on Type-I progressively hybrid censored data from exponential distributions. Stat Methodol 10(1):128–150

    Article  MathSciNet  MATH  Google Scholar 

  • Cramer E, Burkschat M, Górny J (2016) On the exact distribution of the MLEs based on Type-II progressively hybrid censored data from exponential distributions. J Stat Comput Simul 86(10):2036–2052

    Article  MathSciNet  Google Scholar 

  • Curry HB, Schoenberg IJ (1947) On spline distributions and their limits: the Polya distribution functions. Bull Am Math Soc 53:1114

    Google Scholar 

  • de Boor C (2001) A practical guide to splines, revised edn. Springer, Berlin, New York

    MATH  Google Scholar 

  • Epstein B (1954) Truncated life tests in the exponential case. Ann Math Stat 25(3):555–564

    Article  MathSciNet  MATH  Google Scholar 

  • Górny J (2017) A new approach to hybrid censoring. PhD Thesis, RWTH Aachen University, Aachen, Germany. https://doi.org/10.18154/RWTH-2017-05192

  • Górny J, Cramer E (2016) Exact likelihood inference for exponential distributions under generalized progressive hybrid censoring schemes. Stat Methodol 29:70–94

    Article  MathSciNet  Google Scholar 

  • Górny J, Cramer E (2017a) From B-spline representations to gamma representations in hybrid censoring. Stat Pap. https://doi.org/10.1007/s00362-016-0866-4

    Google Scholar 

  • Górny J, Cramer E (2017b) Type-I hybrid censoring of uniformly distributed lifetimes. Commun Stat Theory Methods (accepted)

  • Huang W-T, Yang K-C (2010) A new hybrid censoring scheme and some of its properties. Tamsui Oxf J Math Sci 26(4):355–367

    MathSciNet  MATH  Google Scholar 

  • Panahi H, Sayyareh A (2015) Estimation and prediction for a unified hybrid-censored Burr Type XII distribution. J Stat Comput Simul 86(1):55–73

    Article  MathSciNet  Google Scholar 

  • Park S, Balakrishnan N (2012) A very flexible hybrid censoring scheme and its Fisher information. J Stat Comput Simul 82(1):41–50

    Article  MathSciNet  MATH  Google Scholar 

  • Rad AH, Izanlo M (2011) An EM algorithm for estimating the parameters of the generalized exponential distribution under unified hybrid censored data. J Stat Res Iran 8(2):149–162

    Google Scholar 

  • Schumaker LL (2007) Spline functions: basic theory, 3rd edn. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, 52056, Aachen, Germany

    Julian Górny & Erhard Cramer

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  1. Julian Górny
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  2. Erhard Cramer
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Correspondence to Julian Górny.

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Górny, J., Cramer, E. Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring. Metrika 81, 173–210 (2018). https://doi.org/10.1007/s00184-017-0639-7

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  • DOI: https://doi.org/10.1007/s00184-017-0639-7

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