On a new class of tests for the Pareto distribution using Fourier methods

TL;DR

This paper introduces new Fourier-based goodness-of-fit tests for the Pareto distribution, demonstrating their high power and consistency through theoretical derivations and Monte Carlo simulations.

Contribution

The paper develops novel $U$ and $V$ statistics for testing Pareto distribution using characteristic functions, with simple computation and proven consistency.

Findings

Tests show high power against fixed alternatives

Effective in detecting local alternatives and mixtures

Validated with real data example

Abstract

We propose new classes of tests for the Pareto type I distribution using the empirical characteristic function. These tests are $U$ and $V$ statistics based on a characterisation of the Pareto distribution involving the distribution of the sample minimum. In addition to deriving simple computational forms for the proposed test statistics, we prove consistency against a wide range of fixed alternatives. A Monte Carlo study is included in which the newly proposed tests are shown to produce high powers. These powers include results relating to fixed alternatives as well as local powers against mixture distributions. The use of the proposed tests is illustrated using an observed data set.