A Seneta’s Conjecture and the Williamson Transform

Abstract:

Considering slowly varying functions (SVF), Seneta in 2019 conjectured the following implication, for α ≥ 1, ^∫<inf>0</inf>^x y^α−¹(1 − F(y))dy is SVF → ^∫<inf>0</inf>^x y^αdF(y) is SVF, as x → ∞, where F(x) is a cumulative distribution function on [0, ∞). 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.

Año de publicación:

2023

Keywords:

• De Haan class
• Regular variation
• Truncated moments
• Williamson transform

Fuente:

scopus