On classes of consistent tests for the Type I Pareto distribution based on a characterization involving order statistics

• Published in: Statistics (Berlin, DDR) Vol. 58; no. 3; pp. 521 - 551
• Main Authors: Ngatchou-Wandji, Joseph, Nombebe, Thobeka, Santana, Leonard, Allison, James
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03-05-2024; Taylor & Francis Ltd; Taylor & Francis: STM, Behavioural Science and Public Health Titles
• Subjects: characteristic function; characterization; consistency; Goodness of fit; Mathematics; Pareto distribution; Pareto optimum; Statistical tests; Statistics; Characteristic function; Characterization; Pareto distribution; Goodness-of-fit; Consistency
• ISSN: 0233-1888; 1029-4910
• DOI: 10.1080/02331888.2024.2347342

We propose new classes of goodness-of-fit tests for the Pareto Type I distribution. These tests are based on a characterization of the Pareto distribution involving order statistics. We derive the limiting null distribution of the tests and also show that the tests are consistent against fixed alternatives. The finite-sample performance of the newly proposed tests are evaluated and compared to some of the existing tests, where it is found that the new tests are competitive in terms of powers. The paper concludes with an application to a real world data set, namely the earnings of the 22 highest paid participants in the inaugural season of LIV golf.