In this paper, we proposed a new nonparametric test for discussing the problem of testing that two life distributions F and G are identical against the alternative that F is more harmonic new better than used in expectation (HNBUE) than G. The asymptotic normality of the proposed test is established and the asymptotic null variance is estimated from the data. Pitman asymptotic relative efficiencies (PARE) of proposed test are calculated for different distributions. Another test proposed for testing that two life distributions F and G are identical against the alternative that F is more HNBUE than G at a specific age . The asymptotic normality of proposed test is established and the asymptotic null variance is estimated. Pitman asymptotic efficiencies (PAE) of proposed test are calculated for different distributions. A numerical example is presented for illustrative our test purpose.
Keywords: Asymptotic normal, HNBUE, Pitman asymptotic efficiency, U-statistic.
