Poisson approximations for 2-dimensional patterns |
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| Authors: | James C Fu Markos V Koutras |
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| Institution: | (1) Department of Statistics, The University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada;(2) Department of Mathematics, Section of Statistics and O.R., University of Athens, Panepistemiopolis, 157 10 Athens, Greece |
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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.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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| Keywords: | Random matrix Bernoulli random variables Poisson approximation patterns consecutive-k-out-of-n:F system |
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