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Matching fixed rectangles in 2-dimension

Author

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  • Sheng, Ke-Ning
  • Naus, Joseph I.

Abstract

For each element Xi,j(1 [less-than-or-equals, slant] i [less-than-or-equals, slant] M, 1 [less-than-or-equals, slant] j [less-than-or-equals, slant] T) in an M by T 2-dimensional random rectangular lattice, let the Xi,j's be independently, identically distributed and P{Xi,j = 1} = p [epsilon] (0, 1), P{Xi,j [not equal to] 1} = 1 - p. We find the probability, ifP{n, k vb M, T}, that there exists a smaller fixed (n by k) rectangle of all 1's in the M by T random rectangular lattice. Exact results for the special cases M = n,n + 1,n + 2 and approximations and upper bounds of the probability in the general case are given and evaluated.

Suggested Citation

  • Sheng, Ke-Ning & Naus, Joseph I., 1996. "Matching fixed rectangles in 2-dimension," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 83-90, January.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:1:p:83-90
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    Cited by:

    1. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.

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