Geodesic
Sharp mean-variance inequalities for quantiles of distributions determined by convex and star orders
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 320-338

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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: convex order, star order, monotone density (in average), monotone failure rate (in average), projection, convex cone.
Mots-clés : quantile 
@article{TVP_2002_47_2_a6,
     author = {T. Rychlik},
     title = {Sharp mean-variance inequalities for quantiles of distributions determined by convex and star orders},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {320--338},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a6/}
}
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T. Rychlik. Sharp mean-variance inequalities for quantiles of distributions determined by convex and star orders. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 320-338. http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a6/