On the stability of a characterization by the lack of memory property
An useful and interesting characterization of the Weibull distribution is its lack of memory (of order α) property, i.e., P(X ≥ (xα + yα)1/α|X ≥ y) = P(X ≥ x) for all x, y ≥ 0. The characterization holds even in the case when it is required to fulfil this relation not on the entire semi-axis {y|y...
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| Language: | English |
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Vilnius University Press
2003-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/32566 |
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| _version_ | 1832593209294848000 |
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| author | Romanas Januškevičius |
| author_facet | Romanas Januškevičius |
| author_sort | Romanas Januškevičius |
| collection | DOAJ |
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An useful and interesting characterization of the Weibull distribution is its lack of memory (of order α) property, i.e., P(X ≥ (xα + yα)1/α|X ≥ y) = P(X ≥ x) for all x, y ≥ 0. The characterization holds even in the case when it is required to fulfil this relation not on the entire semi-axis {y|y ≥ 0}, but only at two incommensurable points y1 and y2. The stability estimation in this characterization is analyzed.
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| format | Article |
| id | doaj-art-97121ec122cc4f50b83dc0cbd86048d5 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2003-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-97121ec122cc4f50b83dc0cbd86048d52025-01-20T18:17:17ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2003-12-0143spec.10.15388/LMR.2003.32566On the stability of a characterization by the lack of memory propertyRomanas Januškevičius0Institute of Mathematics and Informatics An useful and interesting characterization of the Weibull distribution is its lack of memory (of order α) property, i.e., P(X ≥ (xα + yα)1/α|X ≥ y) = P(X ≥ x) for all x, y ≥ 0. The characterization holds even in the case when it is required to fulfil this relation not on the entire semi-axis {y|y ≥ 0}, but only at two incommensurable points y1 and y2. The stability estimation in this characterization is analyzed. https://www.journals.vu.lt/LMR/article/view/32566 |
| spellingShingle | Romanas Januškevičius On the stability of a characterization by the lack of memory property Lietuvos Matematikos Rinkinys |
| title | On the stability of a characterization by the lack of memory property |
| title_full | On the stability of a characterization by the lack of memory property |
| title_fullStr | On the stability of a characterization by the lack of memory property |
| title_full_unstemmed | On the stability of a characterization by the lack of memory property |
| title_short | On the stability of a characterization by the lack of memory property |
| title_sort | on the stability of a characterization by the lack of memory property |
| url | https://www.journals.vu.lt/LMR/article/view/32566 |
| work_keys_str_mv | AT romanasjanuskevicius onthestabilityofacharacterizationbythelackofmemoryproperty |