New Classes of Tests for The Pareto Distribution Based on A Conditional Expectation Characterisation

Abstract

here are relatively few goodness-of-fit tests specifically developed for the Pareto distribution when compared to other well-known distributions like the normal or exponential distributions. This is the case even though there are a host of practical applications where it would be required to first check the assumption that the data were realised from a Pareto distribution. We propose and investigate new goodness-of-fit tests for the Pareto Type I distribution based on a specific conditional expectation that characterises the Pareto distribution. Currently, the literature contains no other tests for the Pareto distribution based on conditional expectation. We conduct a thorough Monte Carlo power study in order to assess the finite sample performance of the newly developed tests using various estimation methods. The results from the simulation study show that the newly proposed tests are competitive in terms of power performance when compared to some existing tests. It also shows that the majority of tests produce their highest powers when the unknown shape parameter is estimated by the method of moments. A practical example, where we consider the annual salaries of English Premier League football players for two consecutive seasons, is also included to illustrate the use of the newly proposed tests. We find that the salaries in the 2021-2022 season can be adequately modelled with the Pareto distribution, but not the salaries for the 2022-2023 season.