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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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