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On some exact distributional results based on Type-I progressively hybrid censored data from exponential distributions. (English) Zbl 1365.62061
Summary: In this paper, we present an approach for deriving the exact distributions of the maximum likelihood estimators (MLEs) of location and scale parameters of a two-parameter exponential distribution when the data are Type-I progressively hybrid censored. In addition to this new result for the two-parameter exponential model, we also obtain much simpler expressions for those cases of Type-I hybrid censored data which have been studied before. Our results are obtained by a new approach based on the spacings of the data. In particular, we show that the density function of the scale estimator can be expressed in terms of $$B$$-spline functions, while the location estimator is seen to have a right-truncated exponential distribution.

##### MSC:
 62E15 Exact distribution theory in statistics 62N02 Estimation in survival analysis and censored data 62N05 Reliability and life testing
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