Log-concavity and log-convexity of moments of averages of i.i.d. random variables
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).
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.06439
- arXiv:
- arXiv:2001.06439
- Bibcode:
- 2020arXiv200106439L
- Keywords:
-
- Mathematics - Probability;
- Mathematics - Combinatorics;
- 05A20;
- 60E15;
- 26D15
- E-Print:
- 8 pages