A Seneta's Conjecture and the Williamson Transform
Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,$$\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$,}$$where $F(x)$ is a cumulative distribution...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2023-09-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_706712_1874b9e9f26269a43add982e3eaf0042.pdf |
| _version_ | 1797666612612956160 |
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| author | Edward Omey Meitner Cadena |
| author_facet | Edward Omey Meitner Cadena |
| author_sort | Edward Omey |
| collection | DOAJ |
| description | Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,$$\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$,}$$where $F(x)$ is a cumulative distribution function on $[0,\infty)$. By applying the Williamson transform, an extension of this conjecture is proved. Complementary results related to this transform and particular cases of this extended conjecture are discussed. |
| first_indexed | 2024-03-11T20:00:56Z |
| format | Article |
| id | doaj.art-e81af5e9a7294ec2a3c71e2fa7541d2d |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-03-11T20:00:56Z |
| publishDate | 2023-09-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-e81af5e9a7294ec2a3c71e2fa7541d2d2023-10-04T08:29:38ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002023-09-0120422724110.22130/scma.2023.1983415.1223706712A Seneta's Conjecture and the Williamson TransformEdward Omey0Meitner Cadena1Dept. MEES, Campus Brussels, KU Leuven, Warmoesberg 26, Brussels, Belgium.DECE, Universidad de las Fuerzas Armadas, Sangolqui, Ecuador.Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,$$\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$,}$$where $F(x)$ is a cumulative distribution function on $[0,\infty)$. By applying the Williamson transform, an extension of this conjecture is proved. Complementary results related to this transform and particular cases of this extended conjecture are discussed.https://scma.maragheh.ac.ir/article_706712_1874b9e9f26269a43add982e3eaf0042.pdfregular variationde haan classtruncated momentswilliamson transform |
| spellingShingle | Edward Omey Meitner Cadena A Seneta's Conjecture and the Williamson Transform Sahand Communications in Mathematical Analysis regular variation de haan class truncated moments williamson transform |
| title | A Seneta's Conjecture and the Williamson Transform |
| title_full | A Seneta's Conjecture and the Williamson Transform |
| title_fullStr | A Seneta's Conjecture and the Williamson Transform |
| title_full_unstemmed | A Seneta's Conjecture and the Williamson Transform |
| title_short | A Seneta's Conjecture and the Williamson Transform |
| title_sort | seneta s conjecture and the williamson transform |
| topic | regular variation de haan class truncated moments williamson transform |
| url | https://scma.maragheh.ac.ir/article_706712_1874b9e9f26269a43add982e3eaf0042.pdf |
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