Comparison of two life distributions on the basis of their percentile residual life functions

Let F and G be life distributions with respective failure rate functions r F and r G and respective 100α‐percentile (0 < α < 1) residual life functions q α, F , and q α, G . Distribution‐free two‐sample tests are proposed for testing H 0 : F = G against H 1,α ,: q α, F ≥ q α, G and H 2 α : q β, F ≥ q β, G for all β ≥ α. This class of tests includes as a special case the test of Kochar (1981) for the alternative H * 2 : r F ≤ r G . A theorem of Govindarajulu (1976) is extended in order to obtain asymptotic normality of the test statistics. The condition q α, F ≥ q α, G is implied by r F ≤ r G and is unrelated to the stochastic ordering F ≤ G ; if F and G are Weibull distributions with respective shape parameters c 1 and c 2 such that 1 ≤ C 1 < C 2 , then q α, F ≥ q α, G for all α larger than a function of the parameters.