  Pareto distributions are widely used models in economics, finance and
actuarial sciences. As a result, a number of goodness-of-fit tests have been
proposed for these distributions in the literature. We provide an overview of
the existing tests for the Pareto distribution, focussing specifically on the
Pareto type I distribution. To date, only a single overview paper on
goodness-of-fit testing for Pareto distributions has been published. However,
the mentioned paper has a much wider scope than is the case for the current
paper as it covers multiple types of Pareto distributions. The current paper
differs in a number of respects. First, the narrower focus on the Pareto type I
distribution allows a larger number of tests to be included. Second, the
current paper is concerned with composite hypotheses compared to the simple
hypotheses (specifying the parameters of the Pareto distribution in question)
considered in the mentioned overview. Third, the sample sizes considered in the
two papers differ substantially.
  In addition, we consider two different methods of fitting the Pareto Type I
distribution; the method of maximum likelihood and a method closely related to
moment matching. It is demonstrated that the method of estimation has a
profound effect, not only on the powers achieved by the various tests, but also
on the way in which numerical critical values are calculated. We show that,
when using maximum likelihood, the resulting critical values are shape
invariant and can be obtained using a Monte Carlo procedure. This is not the
case when moment matching is employed.
  The paper includes an extensive Monte Carlo power study. Based on the results
obtained, we recommend the use of a test based on the phi divergence together
with maximum likelihood estimation.

Methodology;Computation