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From B-spline representations to gamma representations in hybrid censoring

Author

Listed:
  • Julian Górny

    (RWTH Aachen University)

  • Erhard Cramer

    (RWTH Aachen University)

Abstract

We establish an identity that relates B-spline functions to linear combinations of gamma density functions. Utilizing this connection, we illustrate that, for exponentially distributed lifetimes, the distribution of the MLE in various hybrid censoring schemes can be expressed in terms of gamma density functions with simple weights. As an example, representations for the density functions in the case of Type-I sequential, Type-II progressive hybrid, generalized Type-I progressive hybrid, and generalized Type-II progressive hybrid censoring schemes are presented. It turns out that the representations arising from the spacings’ based approach introduced in Cramer and Balakrishnan (Stat Methodol 10:128–150, 2013) are more compact than those available in the literature so far.

Suggested Citation

  • Julian Górny & Erhard Cramer, 2019. "From B-spline representations to gamma representations in hybrid censoring," Statistical Papers, Springer, vol. 60(4), pages 1119-1135, August.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0866-4
    DOI: 10.1007/s00362-016-0866-4
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    References listed on IDEAS

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    1. 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.
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    4. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    5. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    6. S. Gurler, 2012. "On residual lifetimes in sequential (n − k + 1)-out-of-n systems," Statistical Papers, Springer, vol. 53(1), pages 23-31, February.
    7. Soltani, Ahmad Reza & Roozegar, Rasool, 2012. "On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1012-1020.
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