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Poisson approximations for 2-dimensional patterns

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Abstract

LetX=(X ij) n×n be a random matrix whose elements are independent Bernoulli random variables, taking the values 0 and 1 with probabilityq ij andp ij (p ij+q ij=1) respectively. Upper and lower bounds for the probabilities ofm non-overlapping occurrences of a square submatrix with all its elements being equal to 1, are obtained. Some Poisson convergence theorems are established forn → ∞. Numerical results indicate that the proposed bounds perform very well, even for moderate and small values ofn.

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Authors and Affiliations

  1. Department of Statistics, The University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    James C. Fu

  2. Department of Mathematics, Section of Statistics and O.R., University of Athens, Panepistemiopolis, 157 10, Athens, Greece

    Markos V. Koutras

Authors
  1. James C. Fu
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  2. Markos V. Koutras
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Additional information

This work is supported in part by the Natural Science and Engineering Research Council of Canada under Grant NSERC A-9216.

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Fu, J.C., Koutras, M.V. Poisson approximations for 2-dimensional patterns. Ann Inst Stat Math 46, 179–192 (1994). https://doi.org/10.1007/BF00773602

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  • DOI: https://doi.org/10.1007/BF00773602

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