Geodesic
Log-concavity and log-convexity of moments of averages of i.i.d. random variables
Canadian mathematical bulletin, Tome 65 (2022) no. 2, pp. 271-278

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DOI

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).
DOI : 10.4153/S0008439521000254
Mots-clés : Log-convexity, log-concavity, moment comparison, sums of independent random variables 
Lamkin, Philip; Tkocz, Tomasz. Log-concavity and log-convexity of moments of averages of i.i.d. random variables. Canadian mathematical bulletin, Tome 65 (2022) no. 2, pp. 271-278. doi: 10.4153/S0008439521000254
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     title = {Log-concavity and log-convexity of moments of averages of i.i.d. random variables},
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     year = {2022},
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     doi = {10.4153/S0008439521000254},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000254/}
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