Gaussian approximation to bivariate rayleigh distributions

Abstract

Let X = (X₁...X_M] Y = (Y₁...Y_N] r₁ = [X], and r₂ =[Y], where M<N {[X₁]...[X_M,Y_M] are independent standard Gaussian vecrors having the correlations [P₁...P_M] and {Y_M 1... Y_N} are uncorrelated standard Gaussian variables distributed independently of {[X₁, Y₁],... [X_M, Y_M] A Gaussian approximation to the joint distribution of r₁ and r₂ is based on the normalizing transformation . This approximation is studied numerically in the case of second-order distributions assocoated with a class of stationary Markov Processes. The accuracy of the approximation tends to improve as both M and the arguments of the cumulative distribution function increse. In all cases studied the approximate probabilities differ from actual probabilities at most by 0.01 units provided M>=2

†Supported in part by the National Institutes of Health through Research career Development Award No.5-K03-GM37209-05, and in part by the Office of Naval Research, Contract N00014-72-A-0136-0003. Reproduction in whole or in part is permitted for any purpose of the United States Government

†Supported in part by the National Institutes of Health through Research career Development Award No.5-K03-GM37209-05, and in part by the Office of Naval Research, Contract N00014-72-A-0136-0003. Reproduction in whole or in part is permitted for any purpose of the United States Government

Notes

†Supported in part by the National Institutes of Health through Research career Development Award No.5-K03-GM37209-05, and in part by the Office of Naval Research, Contract N00014-72-A-0136-0003. Reproduction in whole or in part is permitted for any purpose of the United States Government