On the stability of one characterization of the stable distributions
As early as 1923, Georg P6lya wrote: ``The Gaussian error law possesses the property that it remains valid under a linear combination of errors. The Gaussian error law can be characterized by this property to some extent – it is the only law that admits steadiness with respect to linear combination...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2001-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/34743 |
| _version_ | 1797198353311727616 |
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| author | Olga Yanushkevichiene Romanas Yanushkevichius |
| author_facet | Olga Yanushkevichiene Romanas Yanushkevichius |
| author_sort | Olga Yanushkevichiene |
| collection | DOAJ |
| description |
As early as 1923, Georg P6lya wrote: ``The Gaussian error law possesses the property that it remains valid under a linear combination of errors. The Gaussian error law can be characterized by this property to some extent – it is the only law that admits steadiness with respect to linear combinations of errors''. The idea of using linear combinations of random variables to characterize the stable distributions has been extended by P. Levy. We investigate the stability of this characterization.
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| first_indexed | 2024-04-24T06:58:31Z |
| format | Article |
| id | doaj.art-37176eb8d2734ab0aa242111b6d0e492 |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-04-24T06:58:31Z |
| publishDate | 2001-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-37176eb8d2734ab0aa242111b6d0e4922024-04-22T09:04:29ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2001-12-0141spec.10.15388/LMR.2001.34743On the stability of one characterization of the stable distributionsOlga Yanushkevichiene0Romanas Yanushkevichius1Institute of Mathematics and InformaticsInstitute of Mathematics and Informatics As early as 1923, Georg P6lya wrote: ``The Gaussian error law possesses the property that it remains valid under a linear combination of errors. The Gaussian error law can be characterized by this property to some extent – it is the only law that admits steadiness with respect to linear combinations of errors''. The idea of using linear combinations of random variables to characterize the stable distributions has been extended by P. Levy. We investigate the stability of this characterization. https://www.zurnalai.vu.lt/LMR/article/view/34743 |
| spellingShingle | Olga Yanushkevichiene Romanas Yanushkevichius On the stability of one characterization of the stable distributions Lietuvos Matematikos Rinkinys |
| title | On the stability of one characterization of the stable distributions |
| title_full | On the stability of one characterization of the stable distributions |
| title_fullStr | On the stability of one characterization of the stable distributions |
| title_full_unstemmed | On the stability of one characterization of the stable distributions |
| title_short | On the stability of one characterization of the stable distributions |
| title_sort | on the stability of one characterization of the stable distributions |
| url | https://www.zurnalai.vu.lt/LMR/article/view/34743 |
| work_keys_str_mv | AT olgayanushkevichiene onthestabilityofonecharacterizationofthestabledistributions AT romanasyanushkevichius onthestabilityofonecharacterizationofthestabledistributions |