Exponentiality versus generalized Pareto — a resistant and robust test
Using resistant and robust methods we propose the statistic Tn = (FU −M)/(M −FL) for testing exponentiality versus generalized Pareto, where FU , FL and M are, respectively, the upper and lower fourths and the median of a random sample of size n. The statistic Tn is based on the statistic Vn = (Xn:...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2004-06-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/6 |
| _version_ | 1798036867444113408 |
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| author | M. F. Brilhante |
| author_facet | M. F. Brilhante |
| author_sort | M. F. Brilhante |
| collection | DOAJ |
| description |
Using resistant and robust methods we propose the statistic Tn = (FU −M)/(M −FL) for testing exponentiality versus generalized Pareto, where FU , FL and M are, respectively, the upper and lower fourths and the median of a random sample of size n. The statistic Tn is based on the statistic Vn = (Xn:n−M)/(M −X1:n) used by Gomes (1982) to discriminate extremal models in a similar context but with a higher breakdown point. The simulated power of Tn is compared with the simulated power of Un =Xn:n/M and Vn, which can also be used to test the exponential behaviour of the sample data. Although we observe that the power of Tn is lower than the power of Un and Vn, we show that the performance of the first test is better than the performance of the two other tests when compared to broadened situations and mixtures commonly used to evaluate resistance and robustness.
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| first_indexed | 2024-04-11T21:18:52Z |
| format | Article |
| id | doaj.art-b148d290169b4fe8b3ffdf2d961b4c48 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-11T21:18:52Z |
| publishDate | 2004-06-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-b148d290169b4fe8b3ffdf2d961b4c482022-12-22T04:02:44ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712004-06-012110.57805/revstat.v2i1.6Exponentiality versus generalized Pareto — a resistant and robust testM. F. Brilhante0University of Azores Using resistant and robust methods we propose the statistic Tn = (FU −M)/(M −FL) for testing exponentiality versus generalized Pareto, where FU , FL and M are, respectively, the upper and lower fourths and the median of a random sample of size n. The statistic Tn is based on the statistic Vn = (Xn:n−M)/(M −X1:n) used by Gomes (1982) to discriminate extremal models in a similar context but with a higher breakdown point. The simulated power of Tn is compared with the simulated power of Un =Xn:n/M and Vn, which can also be used to test the exponential behaviour of the sample data. Although we observe that the power of Tn is lower than the power of Un and Vn, we show that the performance of the first test is better than the performance of the two other tests when compared to broadened situations and mixtures commonly used to evaluate resistance and robustness. https://revstat.ine.pt/index.php/REVSTAT/article/view/6generalized Pareto distributionbreakdown pointresistancerobustnessbroadened situationsmixtures |
| spellingShingle | M. F. Brilhante Exponentiality versus generalized Pareto — a resistant and robust test Revstat Statistical Journal generalized Pareto distribution breakdown point resistance robustness broadened situations mixtures |
| title | Exponentiality versus generalized Pareto — a resistant and robust test |
| title_full | Exponentiality versus generalized Pareto — a resistant and robust test |
| title_fullStr | Exponentiality versus generalized Pareto — a resistant and robust test |
| title_full_unstemmed | Exponentiality versus generalized Pareto — a resistant and robust test |
| title_short | Exponentiality versus generalized Pareto — a resistant and robust test |
| title_sort | exponentiality versus generalized pareto a resistant and robust test |
| topic | generalized Pareto distribution breakdown point resistance robustness broadened situations mixtures |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/6 |
| work_keys_str_mv | AT mfbrilhante exponentialityversusgeneralizedparetoaresistantandrobusttest |