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Limit distributions of sums of m-dependent Bernoulli random variables
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  • Published: June 1989

Limit distributions of sums of m-dependent Bernoulli random variables

  • William N. Hudson1,
  • Howard G. Tucker2 &
  • Jerry A. Veeh1 

Probability Theory and Related Fields volume 82, pages 9–17 (1989)Cite this article

  • 284 Accesses

  • 10 Citations

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Summary

The set of limit distributions of row sums of a triangular array of Bernoulli random variables which is strictly stationary and m-dependent in each row is characterized. Necessary and sufficient conditions for the convergence of the row sums to a given limit distribution are found. The case of convergence to a Poisson distribution is given special attention.

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References

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  3. Galambos, J.: Advanced probability theory. New York and Basel: Marcel Dekker, Inc. 1988

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  4. Krieger, H.A.: A new look at Bergström's theorem on convergence in distribution for sums of dependent random variables. Isr. J. Math. 47, 32–64 (1984)

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  5. Teicher, H.: On the multivariate poisson distribution. Skand. Akt. 37, 1–9 (1954)

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, Auburn University, 36849, Alabama, USA

    William N. Hudson & Jerry A. Veeh

  2. Dept. of Mathematics, University of California, 92717, Irvine, CA, USA

    Howard G. Tucker

Authors
  1. William N. Hudson
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  2. Howard G. Tucker
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  3. Jerry A. Veeh
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Cite this article

Hudson, W.N., Tucker, H.G. & Veeh, J.A. Limit distributions of sums of m-dependent Bernoulli random variables. Probab. Th. Rel. Fields 82, 9–17 (1989). https://doi.org/10.1007/BF00340009

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  • Received: 15 February 1987

  • Issue Date: June 1989

  • DOI: https://doi.org/10.1007/BF00340009

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Poisson Distribution
  • Limit Distribution
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