This article is cited in 1 paper

Short Communications

Estimates for moduli of smoothness of distribution functions

J. A. Adell, A. Lekuona

University of Zaragoza

Abstract: 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.

Received: 22.11.2004

Language: English

DOI: 10.4213/tvp14

 English version: Theory of Probability and its Applications, 2008, 52:1, 148–152

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