Analyzing a Seneta's conjecture by using the Williamson transform
Abstract
Considering slowly varying functions (SVF), Seneta in 2019 conjectured the following implication, for α≥1, ∫0x yα-1(1-F(y))dy is SVF\ \ ∫[0,x]yαdF(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.
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