Inference about the Tail of a Distribution: Improvementon the Hill Estimator
The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this brief note, we propose an improved estimator which is simple...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/924013 |
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| _version_ | 1832568376674746368 |
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| author | Jean Nuyts |
| author_facet | Jean Nuyts |
| author_sort | Jean Nuyts |
| collection | DOAJ |
| description | The Hill estimator is often used to infer the power behavior in tails of
experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this brief note, we propose an improved estimator which is simple and coherent and often provides an efficient remedy in the bad situations, especially when the distribution is decreasing slowly, when the data is restricted by external cuts to lie within a finite domain, or even when the distribution is increasing. |
| format | Article |
| id | doaj-art-945547ff473949309ebd9aa184dee131 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-945547ff473949309ebd9aa184dee1312025-02-03T00:59:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/924013924013Inference about the Tail of a Distribution: Improvementon the Hill EstimatorJean Nuyts0Department of Theoretical and Mathematical Physics, Université de Mons, 20 Place du Parc, 7000 Mons, BelgiumThe Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this brief note, we propose an improved estimator which is simple and coherent and often provides an efficient remedy in the bad situations, especially when the distribution is decreasing slowly, when the data is restricted by external cuts to lie within a finite domain, or even when the distribution is increasing.http://dx.doi.org/10.1155/2010/924013 |
| spellingShingle | Jean Nuyts Inference about the Tail of a Distribution: Improvementon the Hill Estimator International Journal of Mathematics and Mathematical Sciences |
| title | Inference about the Tail of a Distribution: Improvementon the Hill Estimator |
| title_full | Inference about the Tail of a Distribution: Improvementon the Hill Estimator |
| title_fullStr | Inference about the Tail of a Distribution: Improvementon the Hill Estimator |
| title_full_unstemmed | Inference about the Tail of a Distribution: Improvementon the Hill Estimator |
| title_short | Inference about the Tail of a Distribution: Improvementon the Hill Estimator |
| title_sort | inference about the tail of a distribution improvementon the hill estimator |
| url | http://dx.doi.org/10.1155/2010/924013 |
| work_keys_str_mv | AT jeannuyts inferenceaboutthetailofadistributionimprovementonthehillestimator |