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From B-spline representations to gamma representations in hybrid censoring

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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.

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Authors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, D-52062, 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 Erhard Cramer.

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Górny, J., Cramer, E. From B-spline representations to gamma representations in hybrid censoring. Stat Papers 60, 1119–1135 (2019). https://doi.org/10.1007/s00362-016-0866-4

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  • DOI: https://doi.org/10.1007/s00362-016-0866-4

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