On lower bounds for the variance of functions of random variables with weighted distributions

Abstract

In this paper, based on the obtained characterization via the lower bounds for the variance of a function of random variable X, we nd a characterization of the weighted function corresponding to density function f(x), in terms of Cherno-type inequalities. Subsequently, by using the new characterization, we derive the lower bounds for the variance of a function of the weighted random variable. Moreover, assuming that X is DFR [decreasing failure rate] we nd an lower bound for the variance of this function with specific weight functions.