Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations
Using highly precise and accurate Monte Carlo simulations of 20,000,000 replications and 102 independent simulation experiments with extremely low simulation errors and total uncertainties, we evaluated the performance of four single outlier discordancy tests (Grubbs test N2, Dixon test N8, skewness...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/746451 |
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| author | Surendra P. Verma Lorena Díaz-González Mauricio Rosales-Rivera Alfredo Quiroz-Ruiz |
| author_facet | Surendra P. Verma Lorena Díaz-González Mauricio Rosales-Rivera Alfredo Quiroz-Ruiz |
| author_sort | Surendra P. Verma |
| collection | DOAJ |
| description | Using highly precise and accurate Monte Carlo simulations of 20,000,000 replications and 102 independent simulation experiments with extremely low simulation errors and total uncertainties, we evaluated the performance of four single outlier discordancy tests (Grubbs test N2, Dixon test N8, skewness test N14, and kurtosis test N15) for normal samples of sizes 5 to 20. Statistical contaminations of a single observation resulting from parameters called δ from ±0.1 up to ±20 for modeling the slippage of central tendency or ε from ±1.1 up to ±200 for slippage of dispersion, as well as no contamination (δ=0 and ε=±1), were simulated. Because of the use of precise and accurate random and normally distributed simulated data, very large replications, and a large number of independent experiments, this paper presents a novel approach for precise and accurate estimations of power functions of four popular discordancy tests and, therefore, should not be considered as a simple simulation exercise unrelated to probability and statistics. From both criteria of the Power of Test proposed by Hayes and Kinsella and the Test Performance Criterion of Barnett and Lewis, Dixon test N8 performs less well than the other three tests. The overall performance of these four tests could be summarized as N2≅N15>N14>N8. |
| format | Article |
| id | doaj-art-9cb26a1174a94a8fafd4ab60e80e8b38 |
| institution | DOAJ |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-9cb26a1174a94a8fafd4ab60e80e8b382025-08-20T03:19:50ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/746451746451Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo SimulationsSurendra P. Verma0Lorena Díaz-González1Mauricio Rosales-Rivera2Alfredo Quiroz-Ruiz3Departamento de Sistemas Energéticos, Instituto de Energías Renovables, Universidad Nacional Autónoma de México, 62580 Temixco, MOR, MexicoFacultad de Ciencias, Universidad Autónoma del Estado de Morelos, 62209 Cuernavaca, MOR, MexicoPosgrado en Ciencias, Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, 62209 Cuernavaca, MOR, MexicoDepartamento de Computación, Instituto de Energías Renovables, Universidad Nacional Autónoma de México, 62580 Temixco, MOR, MexicoUsing highly precise and accurate Monte Carlo simulations of 20,000,000 replications and 102 independent simulation experiments with extremely low simulation errors and total uncertainties, we evaluated the performance of four single outlier discordancy tests (Grubbs test N2, Dixon test N8, skewness test N14, and kurtosis test N15) for normal samples of sizes 5 to 20. Statistical contaminations of a single observation resulting from parameters called δ from ±0.1 up to ±20 for modeling the slippage of central tendency or ε from ±1.1 up to ±200 for slippage of dispersion, as well as no contamination (δ=0 and ε=±1), were simulated. Because of the use of precise and accurate random and normally distributed simulated data, very large replications, and a large number of independent experiments, this paper presents a novel approach for precise and accurate estimations of power functions of four popular discordancy tests and, therefore, should not be considered as a simple simulation exercise unrelated to probability and statistics. From both criteria of the Power of Test proposed by Hayes and Kinsella and the Test Performance Criterion of Barnett and Lewis, Dixon test N8 performs less well than the other three tests. The overall performance of these four tests could be summarized as N2≅N15>N14>N8.http://dx.doi.org/10.1155/2014/746451 |
| spellingShingle | Surendra P. Verma Lorena Díaz-González Mauricio Rosales-Rivera Alfredo Quiroz-Ruiz Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations The Scientific World Journal |
| title | Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations |
| title_full | Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations |
| title_fullStr | Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations |
| title_full_unstemmed | Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations |
| title_short | Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations |
| title_sort | comparative performance of four single extreme outlier discordancy tests from monte carlo simulations |
| url | http://dx.doi.org/10.1155/2014/746451 |
| work_keys_str_mv | AT surendrapverma comparativeperformanceoffoursingleextremeoutlierdiscordancytestsfrommontecarlosimulations AT lorenadiazgonzalez comparativeperformanceoffoursingleextremeoutlierdiscordancytestsfrommontecarlosimulations AT mauriciorosalesrivera comparativeperformanceoffoursingleextremeoutlierdiscordancytestsfrommontecarlosimulations AT alfredoquirozruiz comparativeperformanceoffoursingleextremeoutlierdiscordancytestsfrommontecarlosimulations |