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Contents of PMS, Vol. 36, Fasc. 1,
pages 47 - 57
 

ON THE ORDER OF APPROXIMATION IN THE RANDOM CENTRAL LIMIT THEOREM FOR m -DEPENDENT RANDOM VARIABLES

B. L. S. Prakasa Rao
M. Sreehari

Abstract: We consider a random number N n of m -dependent random variables X k with a common distribution and the partial sums S = ∑Nn X Nn j=1 j , where the random variable N n is independent of the sequence of random variables (X ,k ≥ 1) k for every n ≥ 1. Under certain conditions on the random variables X k and N , n we obtain the limit distribution of the sequence S Nn and the corresponding rate of convergence after suitable normalization.

2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary: 60G99.

Keywords and phrases: Random central limit theorem, m -depen-dent random variables, Berry–Esseen type bound, approximation.

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