Suppose that X, Y are positive random variables and m is a numerical (commutative) mean. We prove that the inequality E(m(X, Y )) leq m(E(X ), E(Y )) 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.

Gibilisco, P., Hansen, F. (2017). An inequality for expectation of means of positive random variables. ANNALS OF FUNCTIONAL ANALYSIS, 8(1), 142-151 [10.1215/20088752-3750087].

An inequality for expectation of means of positive random variables

Gibilisco P.
;
2017-01-01

Abstract

Suppose that X, Y are positive random variables and m is a numerical (commutative) mean. We prove that the inequality E(m(X, Y )) leq m(E(X ), E(Y )) 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.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Con Impact Factor ISI
Numerical means, operator means, concavity, random matrices.
Gibilisco, P., Hansen, F. (2017). An inequality for expectation of means of positive random variables. ANNALS OF FUNCTIONAL ANALYSIS, 8(1), 142-151 [10.1215/20088752-3750087].
Gibilisco, P; Hansen, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215290
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