Covariance inequality and its applications. (English) Zbl 0822.60015

Summary: Let \(X\) be a random variable and \(f(t)\), \(g(t)\) be two non-decreasing real functions. A simple proof is given for the following inequality by the name of ‘covariance inequality’: \(\text{cov }(f(X), g(X)) \geq 0\). The case of equality is investigated in detail, and a few applications regarding some inequalities, variance reduction and correlation are provided. Finally, generalization of the inequality in different directions is discussed.


60E15 Inequalities; stochastic orderings
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