Statistics Papers

Document Type

Journal Article

Date of this Version

11-2006

Publication Source

The American Mathematical Monthly

Volume

113

Issue

9

Start Page

817

Last Page

822

DOI

10.2307/27642063

Abstract

For a positive random variable X, let μα(X) be the αth moment of X. Mark Brown proves that for positive and independent random variables X, Y, F(X + Y) ≥ F(X) + F(Y), where F (X) is the ratio μ-1 over μ-2. We prove this inequality and several generalizations by a method which can be used to prove the Schwarz inequality, but which is not widely appreciated.

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Date Posted: 27 November 2017

This document has been peer reviewed.