Computation of Probability Associated with Anderson–Darling Statistic
The correct application of a statistical test is directly connected with information related to the distribution of data. Anderson–Darling is one alternative used to test if the distribution of experimental data follows a theoretical distribution. The conclusion of the Anderson–D...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-05-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/6/6/88 |
| _version_ | 1828487862111174656 |
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| author | Lorentz Jäntschi Sorana D. Bolboacă |
| author_facet | Lorentz Jäntschi Sorana D. Bolboacă |
| author_sort | Lorentz Jäntschi |
| collection | DOAJ |
| description | The correct application of a statistical test is directly connected with information related to the distribution of data. Anderson–Darling is one alternative used to test if the distribution of experimental data follows a theoretical distribution. The conclusion of the Anderson–Darling test is usually drawn by comparing the obtained statistic with the available critical value, which did not give any weight to the same size. This study aimed to provide a formula for calculation of p-value associated with the Anderson–Darling statistic considering the size of the sample. A Monte Carlo simulation study was conducted for sample sizes starting from 2 to 61, and based on the obtained results, a formula able to give reliable probabilities associated to the Anderson–Darling statistic is reported. |
| first_indexed | 2024-12-11T09:58:24Z |
| format | Article |
| id | doaj.art-c53eb748880a4b4ba1ae7e6c1aca8840 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-11T09:58:24Z |
| publishDate | 2018-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c53eb748880a4b4ba1ae7e6c1aca88402022-12-22T01:12:11ZengMDPI AGMathematics2227-73902018-05-01668810.3390/math6060088math6060088Computation of Probability Associated with Anderson–Darling StatisticLorentz Jäntschi0Sorana D. Bolboacă1Department of Physics and Chemistry, Technical University of Cluj-Napoca, Muncii Blvd. No. 103-105, Cluj-Napoca 400641, RomaniaDepartment of Medical Informatics and Biostatistics, Iuliu Haţieganu University of Medicine and Pharmacy, Louis Pasteur Str., No. 6, Cluj-Napoca 400349, RomaniaThe correct application of a statistical test is directly connected with information related to the distribution of data. Anderson–Darling is one alternative used to test if the distribution of experimental data follows a theoretical distribution. The conclusion of the Anderson–Darling test is usually drawn by comparing the obtained statistic with the available critical value, which did not give any weight to the same size. This study aimed to provide a formula for calculation of p-value associated with the Anderson–Darling statistic considering the size of the sample. A Monte Carlo simulation study was conducted for sample sizes starting from 2 to 61, and based on the obtained results, a formula able to give reliable probabilities associated to the Anderson–Darling statistic is reported.http://www.mdpi.com/2227-7390/6/6/88Anderson–Darling test (AD)probabilityMonte Carlo simulation |
| spellingShingle | Lorentz Jäntschi Sorana D. Bolboacă Computation of Probability Associated with Anderson–Darling Statistic Mathematics Anderson–Darling test (AD) probability Monte Carlo simulation |
| title | Computation of Probability Associated with Anderson–Darling Statistic |
| title_full | Computation of Probability Associated with Anderson–Darling Statistic |
| title_fullStr | Computation of Probability Associated with Anderson–Darling Statistic |
| title_full_unstemmed | Computation of Probability Associated with Anderson–Darling Statistic |
| title_short | Computation of Probability Associated with Anderson–Darling Statistic |
| title_sort | computation of probability associated with anderson darling statistic |
| topic | Anderson–Darling test (AD) probability Monte Carlo simulation |
| url | http://www.mdpi.com/2227-7390/6/6/88 |
| work_keys_str_mv | AT lorentzjantschi computationofprobabilityassociatedwithandersondarlingstatistic AT soranadbolboaca computationofprobabilityassociatedwithandersondarlingstatistic |