Normal approximations for binary lattice systems
- 1 September 1980
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (3) , 674-685
- https://doi.org/10.2307/3212961
Abstract
Consider an array of binary random variables distributed over anm1(n) bym2(n) rectangular lattice and letY1(n) denote the number of pairs of variablesd, units apart and both equal to 1. We show that if the binary variables are independent and identically distributed, then under certain conditionsY(n) = (Y1(n), · ··,Yr(n)) is asymptotically multivariate normal fornlarge 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.Keywords
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