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Abstract
In this thesis the problem under consideration is the unique factorization of a product of non-singular multivariate normal cumulative probability distribution functions for dimensions greater than or equal to three. The problem was stated originally in the univariate and bivariate case by T. W. Anderson and S. G. Ghurye. In this thesis, the trivariate case of the problem is solved when each distribution has non-negative partial correlations with at most one partial correlation being zero. In the general n-variate case, the problem is solved when each distribution has positive partial correlations. The method of solution here consists of estimating an asymptotic behavior of each term in the expression for the mixed partial derivative of the natural log of the product of said distributions. It is shown through analyzing these estimates that the parameters of each individual distribution may be identified in terms of their product.
