Moment inequalities for DVRL distributions, characterization and testing for exponentiality

Our goal in this paper is to establish inequalities for the moments of decreasing variance residual life (DVRL) distributions. As a consequence we derive a new characterization of exponentiality. Then we use two of these inequalities to construct new tests for exponentiality versus DVRL. Pitman’s asymptotic relative efficiency is employed to assess the performance of the tests. For some classes of life distributions our tests are better than, or well comparable with, other available tests. We carried out numerical simulations and produced a table for the critical values of one of the proposed tests.