Given 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.
|Number of pages||5|
|State||Published - Dec 1993|
- absolute central first moment
- convex function