Testing for exponentiality against harmonic new better than used in expectation property of life distributions using kernel method

Department of Statistics and 0. R., College of Science P. 0. Box 2455, King Saud University, Riyadh 11451, Saudi ArabiaA new test for testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential is presented based on the highly popular "Kernel methods" of curve fitting. This new procedure is competitive with old one in the sense of Pitman's asymptotic relative efficiency, easy to compute and does not depend on the choice of either the band width or kernel. It also enjoys good power