On testing order restricted mean residual life functions under censoring

In this paper we consider the problems of testing H_0 : a mean residual life (MRL) is exponential
versus H_1 : it is new better than used in expectation (NBUE), but not exponential
first and then H_0 versus H_2 : it is decreasing MRL (DMRL), but not exponential. The
paper gives a nice chronological summary of the tests developed for these two classes both
for the complete data and incomplete data cases. We have developed a new test for each
class under censoring. Both tests are shown to be consistent in their classes. We have
derived the asymptotic distributions of our test statistics.