This article is cited in 4 papers

Sharp mean-variance inequalities for quantiles of distributions determined by convex and star orders

T. Rychlik

Institute of Mathematics of the Polish Academy of Sciences

Abstract: We establish sharp upper bounds on deviations of quantiles from the mean expressed in standard deviation units for all distributions related to a fixed one in the convex and star orders, and we describe the distributions for which the bounds are attained. We specify the results for the families of distributions with monotone density and failure rate and those with monotone density and failure rate in average.

Keywords: quantile, convex order, star order, monotone density (in average), monotone failure rate (in average), projection, convex cone.

Received: 20.04.2000

Language: English

DOI: 10.4213/tvp3650

 English version: Theory of Probability and its Applications, 2003, 47:2, 269–285

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