ON DISTRIBUTION’S CONSTANT SLOWLY VARYING COMPONENT

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Submitted: 2025-02-28; Published: 2025-02-28

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Abstract

In the present report it is proved that for a priori given numbers ρ∈(1,+∞) and L∈R+=(0,∞) there is a distribution {pn}1∞ with the following properties: {pn}1∞ varies regularly as n→+∞ with exponent (−ρ), exhibits the constant slowly varying component L, and {log⁡pn}1∞ is downward convex.