Quantile-Locating Functions and the Distance Between the Mean and QuantilesStatistica Neerlandica
AbstractGiven a random variable X with finite mean, for each 0 < p < 1, a new sharp bound is found on the distance between a p-quantile of X and its mean in terms of the central absolute first moment of X. The new bounds strengthen the fact that the mean of X is within one standard deviation of any of its medians, as well as a recent quantile-generalization of this fact by O'Cinneide.
Citation InformationD. Gilat and Theodore P. Hill. "Quantile-Locating Functions and the Distance Between the Mean and Quantiles" Statistica Neerlandica Vol. 47 Iss. 4 (1993) p. 279 - 283
Available at: http://works.bepress.com/tphill/17/