Geodesic
Estimates for moduli of smoothness of distribution functions
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 186-190

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We give upper bounds for the usual moduli of smoothness of a distribution function $F$ in terms of its characteristic function $\varphi$. In particular, we complete some known estimates of the concentration function of $F$. Our approach uses a new version of the classical Berry–Esseen smoothing inequality.
Keywords: modulus of smoothness, concentration function, characteristic function, smoothing inequality. 
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     author = {J. A. Adell and A. Lekuona},
     title = {Estimates for moduli of smoothness of distribution functions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {186--190},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2007_52_1_a13/}
}
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J. A. Adell; A. Lekuona. Estimates for moduli of smoothness of distribution functions. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 186-190. http://geodesic.mathdoc.fr/item/TVP_2007_52_1_a13/