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1 results

  • Normal approximations for binary lattice systems

  • Richard J. Kryscio, Roy Saunders, Gerald M. Funk
  • Journal:
    Journal of Applied Probability / Volume 17 / Issue 3 / September 1980
    Published online by Cambridge University Press:
    14 July 2016, pp. 674-685
    Print publication:
    September 1980

  • Consider an array of binary random variables distributed over an m1(n) by m2(n) rectangular lattice and let Y1(n) denote the number of pairs of variables d, units apart and both equal to 1. We show that if the binary variables are independent and identically distributed, then under certain conditions Y(n) = (Y1(n), · ··, Yr(n)) is asymptotically multivariate normal for n large and r finite. This result is extended to versions of a model which provide clustering (repulsion) alternatives to randomness and have clustering (repulsion) parameter values nearly equal to 0. Statistical applications of these results are discussed.