On the order of approximation in the random central limit theorem for m-dependent random variables

  1. B. L. S. Prakasa Rao
  2. M. Sreehari

Abstract

We consider a random number Nn of m-dependent random variables Xk with a common distribution and the partial sums SNn = ∑Nn j=1 Xj , where the random variable Nn is independent of the sequence of random variables {Xk; k ≥ 1} for every n ≥ 1. Under certain conditions on the random variables Xk and Nn; we obtain the limit distribution of the sequence SNn and the corresponding rate of convergence after suitable normalization.

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Probability and Mathematical Statistics

36, z. 1, 2016

Pages from 47 to 57

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