Testing Whether New Is Better Than Used of Specified Age Using Moments Inequalities

The class of “new better than used of a specified age” is a large and practical class of life distributions. Its properties, applicability, and testing was discussed by Hollander, Park and Proschan (1986). Their test, while remaining the yardstick for this class, suffers from weak efficiency and weak power, especially for specified ages below the average age. Thus, it is beneficial to have an alternative testing procedure that would work better for early ages and still work well for later ages. This is exactly the subject of the current note. The test developed here is also simpler than that of Hollander, et. al. (1986).