Revisiting the Memoryless Property - Testing for the Pareto Type I Distribution

We propose new goodness-of-fit tests for the Pareto type I distribution. These tests are based on a multiplicative version of the memoryless property which characterises this distribution. We present the results of a Monte Carlo power study demonstrating that the proposed tests are powerful compare...

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Main Authors: Lethani Ndwandwe, James Allison, Leonard Santana, Jaco Visagie
Format: Article
Language:English
Published: Austrian Statistical Society 2025-02-01
Series:Austrian Journal of Statistics
Online Access:https://www.ajs.or.at/index.php/ajs/article/view/1871
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author Lethani Ndwandwe
James Allison
Leonard Santana
Jaco Visagie
author_facet Lethani Ndwandwe
James Allison
Leonard Santana
Jaco Visagie
author_sort Lethani Ndwandwe
collection DOAJ
description We propose new goodness-of-fit tests for the Pareto type I distribution. These tests are based on a multiplicative version of the memoryless property which characterises this distribution. We present the results of a Monte Carlo power study demonstrating that the proposed tests are powerful compared to existing tests. As a result of independent interest, we demonstrate that tests specifically developed for the Pareto type I distribution substantially outperform tests for exponentiality applied to log-transformed data (since Pareto type I distributed values can be transformed to exponentiality via a simple log-transformation). Specifically, the newly proposed tests based on the multiplicative memoryless property of the Pareto distribution substantially outperform a test based on the memoryless property of the exponential distribution. The practical use of tests is illustrated by testing the hypothesis that two sets of observed golfers' earnings (those of the PGA and LIV tours) are realised from Pareto distributions.
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spelling doaj-art-8478e8461a534872be837e5ef1c4604e2025-08-20T02:03:38ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2025-02-0154210.17713/ajs.v54i2.1871Revisiting the Memoryless Property - Testing for the Pareto Type I DistributionLethani Ndwandwe0James AllisonLeonard SantanaJaco VisagieNorth-West University We propose new goodness-of-fit tests for the Pareto type I distribution. These tests are based on a multiplicative version of the memoryless property which characterises this distribution. We present the results of a Monte Carlo power study demonstrating that the proposed tests are powerful compared to existing tests. As a result of independent interest, we demonstrate that tests specifically developed for the Pareto type I distribution substantially outperform tests for exponentiality applied to log-transformed data (since Pareto type I distributed values can be transformed to exponentiality via a simple log-transformation). Specifically, the newly proposed tests based on the multiplicative memoryless property of the Pareto distribution substantially outperform a test based on the memoryless property of the exponential distribution. The practical use of tests is illustrated by testing the hypothesis that two sets of observed golfers' earnings (those of the PGA and LIV tours) are realised from Pareto distributions. https://www.ajs.or.at/index.php/ajs/article/view/1871
spellingShingle Lethani Ndwandwe
James Allison
Leonard Santana
Jaco Visagie
Revisiting the Memoryless Property - Testing for the Pareto Type I Distribution
Austrian Journal of Statistics
title Revisiting the Memoryless Property - Testing for the Pareto Type I Distribution
title_full Revisiting the Memoryless Property - Testing for the Pareto Type I Distribution
title_fullStr Revisiting the Memoryless Property - Testing for the Pareto Type I Distribution
title_full_unstemmed Revisiting the Memoryless Property - Testing for the Pareto Type I Distribution
title_short Revisiting the Memoryless Property - Testing for the Pareto Type I Distribution
title_sort revisiting the memoryless property testing for the pareto type i distribution
url https://www.ajs.or.at/index.php/ajs/article/view/1871
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