This article is cited in 7 papers

An estimate of the concentration function by the Esseen method

N. P. Salikhov

Essential Administration of Information Systems

Abstract: The paper deals with the Esseen method of obtaining upper estimates for the concentration function of a random variable $X$ in terms of the characteristic function of $X$. Some problems of the parametric optimization of such estimates are solved. Applications are described to the estimation of the probabilities of large deviations of the sums of identically distributed random variables.

Keywords: concentration function, characteristic function, probabilities of large deviations, Poisson summation formula, Esseen inequality, Euler numbers.

Received: 02.08.1993

DOI: 10.4213/tvp3137

 English version: Theory of Probability and its Applications, 1997, 41:3, 504–518

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