Quantile‐locating functions and the distance between the mean and quantiles

D. Gilat*, T. P. Hill

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)279-283
Number of pages5
JournalStatistica Neerlandica
Issue number4
StatePublished - Dec 1993


  • absolute central first moment
  • convex function
  • mean
  • median
  • quantiles


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