Goodness-of-fit to the exponential distribution, focused on Weibull alternatives

The goodness-of-fit technique based on the use of transformed empirical processes (TEPs) is applied to the construction of a test of exponentiality, focused oil Weibull alternatives. The resulting procedure shares some desirable properties with other existing applications of the same technique: (a) the tests are consistent against fixed alternatives, (b) local alternatives belonging to the Weibull family are detected with an asymptotic power that does not differ significantly from the power of a two-sided (non consistent) likely ratio test (LRT), and (c) this asymptotic power is the same already encountered when a quadratic Cramer-von Mises-Watson type test statistic is used to test the fit to a single probability distribution, or to a parametric model with estimation of parameters-In that sense, it is distribution free. In addition, an empirical power study shows that our test has the same level of performance than the best tests in the statistical literature.