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

D. Gilat; T. P. Hill

doi:10.1111/j.1467-9574.1993.tb01424.x

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

D. Gilat^*, T. P. Hill

^*Corresponding author for this work

School of Mathematical Sciences

Georgia Institute of Technology

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 language	English
Pages (from-to)	279-283
Number of pages	5
Journal	Statistica Neerlandica
Volume	47
Issue number	4
DOIs	https://doi.org/10.1111/j.1467-9574.1993.tb01424.x
State	Published - Dec 1993

Keywords

absolute central first moment
convex function
mean
median
quantiles

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10.1111/j.1467-9574.1993.tb01424.x

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KW - convex function

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KW - median

KW - quantiles

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

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Keywords

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