A Scale-Free Goodness-Of-Fit Test for the Exponential Distribution Based on the Gini Statistic

Abstract

Summary The sample Gini index is shown to be a powerful scale-free test of exponentiality against a variety of alternatives. Compared to the maximum likelihood test, the asymptotic relative efficiency of the Gini statistic is 0·69 against gamma and 0·88 against Weibull alternatives. Exact and asymptotic distribution theory is developed. On the basis of good power compared to competing tests, ease of computation, availability of exact critical values and robustness to measurement error, we recommend the Gini statistic as a scale-free goodness-of-fit test for the exponential distribution.