On a Conjecture of Seneta on Regular Variation of Truncated Moments

Kevei, Péter (2021) On a Conjecture of Seneta on Regular Variation of Truncated Moments. PUBLICATIONS DE L INSTITUT MATHEMATIQUE, 109 (123). pp. 77-82. ISSN 0350-1302

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Abstract

In this short note we prove that $h_\beta(x) = \beta \int_0^x y^{\beta-1} \overline F(y) \dd y$ is regularly varying with index $\rho \in [0,\beta)$ if and only if $V_\beta (x) = \int_{[0,x]} y^\beta \dd F(y)$ is regularly varying with the same index. This implies an extended version of a recent conjecture by Seneta (2019).

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