Analysis of power of the classical and robust normality tests against bimodal distribution
The aim of this paper is to compare the power of selected normality tests to detect a bimodal distribution. We use some classical normality tests (the Shapiro-Wilk test, the Lilliefors test, the Anderson-Darling test, the classical Jarque-Bera test and the Jarque-Bera-Urzua test), some robust normal...
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| Format: | Article |
| Language: | English |
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Mendel University Press
2009-01-01
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| Series: | Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis |
| Subjects: | |
| Online Access: | https://acta.mendelu.cz/57/6/0253/ |
| _version_ | 1818265963651399680 |
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| author | Luboš Střelec |
| author_facet | Luboš Střelec |
| author_sort | Luboš Střelec |
| collection | DOAJ |
| description | The aim of this paper is to compare the power of selected normality tests to detect a bimodal distribution. We use some classical normality tests (the Shapiro-Wilk test, the Lilliefors test, the Anderson-Darling test, the classical Jarque-Bera test and the Jarque-Bera-Urzua test), some robust normality tests (the robust Jarque-Bera test and the Medcouple test) and the modified Jarque-Bera tests, where the median instead of the mean is used in the classical Jarque-Bera test statistic. The results of simulation study show that the Anderson-Darling and the Shapiro-Wilk tests outperform the others, especially in small sample sizes. On the other hand the classical Jarque-Bera, the Jarque-Bera-Urzua and robust Jarque-Bera tests are biased, especially in small sample sizes again. Finally, the modification of the Jarque-Bera test leads to increase of power against bimodal distribution. |
| first_indexed | 2024-12-12T19:59:09Z |
| format | Article |
| id | doaj.art-717731f509ae462aaa3b29e58eabbeec |
| institution | Directory Open Access Journal |
| issn | 1211-8516 2464-8310 |
| language | English |
| last_indexed | 2024-12-12T19:59:09Z |
| publishDate | 2009-01-01 |
| publisher | Mendel University Press |
| record_format | Article |
| series | Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis |
| spelling | doaj.art-717731f509ae462aaa3b29e58eabbeec2022-12-22T00:13:48ZengMendel University PressActa Universitatis Agriculturae et Silviculturae Mendelianae Brunensis1211-85162464-83102009-01-0157625326010.11118/actaun200957060253Analysis of power of the classical and robust normality tests against bimodal distributionLuboš Střelec0Ústav statistiky a operačního výzkumu, Mendelova zemědělská a lesnická univerzita v Brně, 613 00 Brno, Česká republikaThe aim of this paper is to compare the power of selected normality tests to detect a bimodal distribution. We use some classical normality tests (the Shapiro-Wilk test, the Lilliefors test, the Anderson-Darling test, the classical Jarque-Bera test and the Jarque-Bera-Urzua test), some robust normality tests (the robust Jarque-Bera test and the Medcouple test) and the modified Jarque-Bera tests, where the median instead of the mean is used in the classical Jarque-Bera test statistic. The results of simulation study show that the Anderson-Darling and the Shapiro-Wilk tests outperform the others, especially in small sample sizes. On the other hand the classical Jarque-Bera, the Jarque-Bera-Urzua and robust Jarque-Bera tests are biased, especially in small sample sizes again. Finally, the modification of the Jarque-Bera test leads to increase of power against bimodal distribution.https://acta.mendelu.cz/57/6/0253/tests of normalityrobust testsMonte Carlo simulationpower comparisonbimodal distribution |
| spellingShingle | Luboš Střelec Analysis of power of the classical and robust normality tests against bimodal distribution Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis tests of normality robust tests Monte Carlo simulation power comparison bimodal distribution |
| title | Analysis of power of the classical and robust normality tests against bimodal distribution |
| title_full | Analysis of power of the classical and robust normality tests against bimodal distribution |
| title_fullStr | Analysis of power of the classical and robust normality tests against bimodal distribution |
| title_full_unstemmed | Analysis of power of the classical and robust normality tests against bimodal distribution |
| title_short | Analysis of power of the classical and robust normality tests against bimodal distribution |
| title_sort | analysis of power of the classical and robust normality tests against bimodal distribution |
| topic | tests of normality robust tests Monte Carlo simulation power comparison bimodal distribution |
| url | https://acta.mendelu.cz/57/6/0253/ |
| work_keys_str_mv | AT lubosstrelec analysisofpoweroftheclassicalandrobustnormalitytestsagainstbimodaldistribution |