Title: A new class of tests for the Pareto distribution based on the empirical characteristic function
Authors: James Allison - Northwest University (South Africa)
Marius Smuts - North-West University (South Africa)
Jaco Visagie - North-West University (South Africa) [presenting]
Abstract: The Pareto Type I distribution is a popular model in economics, finance and actuarial science, especially where phenomena characterised by heavy tails are studied. Due to the popularity of this distribution, goodness-of-fit tests have been developed to test the hypothesis that an observed dataset is compatible with the assumption of being realised from this distribution. Although tests exist for the Pareto distribution, they are few in number compared to those for other distributions such as, for example, the normal and exponential distributions. We propose a class of goodness-of-fit tests for the Pareto Type I distribution based on a characterisation involving the distribution of the sample minimum. The test is based on a weighted L2 norm between empirical characteristic function. A Monte Carlo study, involving the bootstrap, shows that the performance of the newly proposed tests compares favourably to existing tests for the Pareto distribution. A practical example relating to the earnings of professional golfers is included.