On some exact distributional results based on Type-I progressively hybrid censored data from exponential distributions

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 BB-spline functions, while the location estimator is seen to have a right-truncated exponential distribution.