Analyzing a Seneta's conjecture by using the Williamson transform

11/08/2022

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by   Edward Omey, et al.

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Considering slowly varying functions (SVF), Seneta in 2019 conjectured the following implication, for α≥1, ∫_0^x y^α-1(1-F(y))dy is SVF ⟹∫_[0,x]y^αdF(y) is SVF, as x→∞, where F(x) is a cumulative distribution function on [0,∞). Complementary results related to this transform and particular cases of this extended conjecture are discussed.