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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Bibliographic Details
Published in:	Sahand Communications in Mathematical Analysis
Main Authors:	Edward Omey, Meitner Cadena
Format:	Article
Language:	English
Published:	University of Maragheh 2023-09-01
Subjects:	regular variation de haan class truncated moments williamson transform
Online Access:	https://scma.maragheh.ac.ir/article_706712_1874b9e9f26269a43add982e3eaf0042.pdf

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