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Asymptotic normality of the number of values of m-dependent random variables which occur a given number of times

Published/Copyright: March 29, 2011
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Discrete Mathematics and Applications
From the journal Volume 21 Issue 1

Abstract

We consider a stationary sequence x1, x2, . . . , xt, . . . of random variables each of which takes values in the set . Let μr = μr(n, N) be the number of values in the set which occur r times in the first n elements of the sequence. In this paper, we obtain asymptotic formulas for the mean value Eμr(n, N) and the variance Dμr(n, N) and give sufficient conditions for asymptotic normality of the random variables μr(n, N) as n, N → ∞ under the condition that the sequence consists of m-dependent random variables and the parameters of the distribution of the sequence vary in the so-called central domain.

Received: 2010-10-10
Published Online: 2011-03-29
Published in Print: 2011-March

© de Gruyter 2011

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  3. Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components
  4. A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences
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  6. On the semigroups of endomorphisms of direct products of commutative Moufang loops
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https://doi.org/10.1515/dma.2011.002

Articles in the same Issue

  1. On the maximum size of a tree in a random unlabelled unrooted forest
  2. Asymptotic normality of the number of values of m-dependent random variables which occur a given number of times
  3. Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components
  4. A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences
  5. The critical ω-foliated τ-closed formations of finite groups
  6. On the semigroups of endomorphisms of direct products of commutative Moufang loops
  7. The Voronoi polyhedra of the rooted lattice E6 and of its dual lattice
  8. Calculation of the characteristic polynomial of a matrix
  9. A case of insolubility of the problem of equivalence of programs
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