Inference for exponentially distributed lifetimes

In this chapter, the cases of scaled exponential and two-parameter exponential distributions are taken up, wherein exact inferential results become possible. First, the results for the case of Type-I hybrid censoring are developed in detail. Next, the corresponding results for the case of Type-II hybrid censoring are presented. Finally, extensions of these results to the cases of generalized hybrid and unified hybrid censoring cases are detailed. The density functions are expressed in terms of B-spline functions leading to compact expressions. It is illustrated that the modularization approach provides an efficient way to derive the distributions even for very complex hybrid censoring schemes. Some examples, using data from some life-tests, are presented to illustrate all the theoretical results described here.