Goodness-of-Fit Tests for Pareto Distribution Based on a Characterization and their Asymptotics

In this paper we present a new characterization of Pareto distribution and consider goodness of fit tests based on it. We provide an integral and Kolmogorov- Smirnov type statistics based on U-statistics and we calculate Bahadur efficiency for various alternatives. We find locally optimal alternatives for those tests. For small sample sizes we compare the power of those tests with some common goodness of fit tests.