Lobachevskii Journal of Mathematics, Volume (37), No (4), Year (2016-7) , Pages (422-435)

Title : ( On upper bounds for the variance of functions of random variables with weighted distributions )

Authors: faranak goodarzi , Mohammad Amini , Gholam Reza Mohtashami Borzadaran ,

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Abstract

Cacoullos and Papathanasiou (1989) obtained a characterization for the distribution of a random variable via the upper bounds for the variance of a given function of that random variable. In this paper, on the basis of their works, we derive a characterization for the weighted distribution. Subsequently, by using the characterization and in terms of Chernoff-type inequalities, we find the upper bounds for the variance of a given function of the weighted random variable. Moreover, assuming that X is IFR [increasing failure rate] we compute an upper bound for the variance of this function.

Keywords

, Variance bounds, Chernoff inequality, size-biased distribution, logconcave, increasing failure rate.