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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 17, Fasc. 2,
pages 395 - 406
 

SLOW CONVERGENCE TO NORMALITY:

AN EDGEWORTH EXPANSION WITHOUT THIRD MOMENT

L. De Haan
L. Peng

Abstract: Let F be a non-lattice distribution function which lies in the domain of attraction of a normal distribution. Exact uniform convergence rates are obtained for the convergence of the normalized partial sums of i.i.d. random variables with distribution F. The assumptions are

1- F(x)+ F (-x) (- RV (- 1 < r < 0) r-2
and

(1- F (x))/(1- F (x) + F(-x))-- > p (- [0,1] (as x-- > oo ).
For r = -1 somewhat weaker conditions are sufficient.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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