A Scale-Free Goodness-of-Fit Test for the Exponential Distribution Based on the Lorenz Curve

The sample Lorenz curve provides a powerful, easily computed goodness-of-fit test for exponentiality which does not depend on the unknown scale parameter. Exact critical values and asymptotic results are given, which can also be used to test the related hypothesis of randomness on an interval. General limit theorems show that the sample Lorenz curve converges almost surely to the population Lorenz curve and that the standardized Lorenz statistic converges to normality provided the underlying random variable has finite variance. Asymptotic relative efficiencies and Monte Carlo power estimates are also given.