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...
Saved in:
| Main Authors: | , , , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850231156952268800 |
|---|---|
| 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.
|
| format | Article |
| id | doaj-art-8478e8461a534872be837e5ef1c4604e |
| institution | OA Journals |
| issn | 1026-597X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| 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 |
| work_keys_str_mv | AT lethanindwandwe revisitingthememorylesspropertytestingfortheparetotypeidistribution AT jamesallison revisitingthememorylesspropertytestingfortheparetotypeidistribution AT leonardsantana revisitingthememorylesspropertytestingfortheparetotypeidistribution AT jacovisagie revisitingthememorylesspropertytestingfortheparetotypeidistribution |