@article {
author = {Omey, Edward and Cadena, Meitner},
title = {A Seneta's Conjecture and the Williamson Transform},
journal = {Sahand Communications in Mathematical Analysis},
volume = {20},
number = {4},
pages = {227-241},
year = {2023},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2023.1983415.1223},
abstract = {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.},
keywords = {Regular variation,De Haan class,Truncated moments,Williamson transform},
url = {https://scma.maragheh.ac.ir/article_706712.html},
eprint = {https://scma.maragheh.ac.ir/article_706712_1874b9e9f26269a43add982e3eaf0042.pdf}
}