Informatics and Applications

September 2013, Volume 7, Issue 3, pp 102-105

ESTIMATES OF THE RATE OF CONVERGENCE OF THE DISTRIBUTIONS OF SOME RANDOM SUMS TO STABLE LAWS

  • V. Yu. Korolev
  • L. M. Zaks

Abstract

Estimates are presented for the rate of convergence of the distributions of special sums of independent identically distributed random variables with finite variances to symmetric strictly stable laws. The distribution of the random index is assumed to be mixed Poisson in which the mixing distribution is a stable law concentrated on the positive half-line. The absolute constants are written out explicitly.

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