Premium
Quantile‐locating functions and the distance between the mean and quantiles
Author(s) -
Gilat D.,
Hill T. P.
Publication year - 1993
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1993.tb01424.x
Subject(s) - quantile , mathematics , standard deviation , statistics , generalization , sample mean and sample covariance , moment (physics) , absolute deviation , random variable , truncated mean , econometrics , mathematical analysis , physics , classical mechanics , estimator
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.