Log-concavity and log-convexity of moments of averages of i.i.d. random variables
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Published:2021-05-03
Issue:
Volume:
Page:1-8
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. Math. Bull.
Author:
Lamkin Philip,Tkocz Tomasz
Abstract
Abstract
We show that the sequence of moments of order less than 1 of averages of i.i.d. positive random variables is log-concave. For moments of order at least 1, we conjecture that the sequence is log-convex and show that this holds eventually for integer moments (after neglecting the first
$p^2$
terms of the sequence).
Publisher
Canadian Mathematical Society
Subject
General Mathematics