An inequality for expectation of means of positive random variables
Probability
2017-02-22 v1
Abstract
Suppose that are positive random variable and a numerical (commutative) mean. We prove that the inequality holds if and only if the mean is generated by a concave function. With due changes we also prove that the same inequality holds for all operator means in the Kubo-Ando setting. The case of the harmonic mean was proved by C.R. Rao and B.L.S. Prakasa Rao.
Keywords
Cite
@article{arxiv.1608.08671,
title = {An inequality for expectation of means of positive random variables},
author = {Paolo Gibilisco and Frank Hansen},
journal= {arXiv preprint arXiv:1608.08671},
year = {2017}
}