Characterization of distributions through Cauchy-Schwarz inequality

Abstract

In this paper, we obtain bounds for the expected value of selected functions in reliability theory viz. failure rate, mean residual, log-odds rate, aging intensity functions and Glaser's function by Cauchy-Schwarz inequality. In some cases, we give two bounds for the expectation and compare the bounds. By the integral form of the Cauchy-Shwarz inequality, we obtain a lower bound for the expectation involving of aging intensity function. We also characterize a few continuous and discrete distributions.