A NOTE ON THE EVALUATION OF A MULTIVARIATE NORMAL INTEGRAL BY THE METHOD OF DAS
SOUTHERN METHODIST UNIV DALLAS TX DEPT OF STATISTICAL SCIENCE
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Das 1956 presents a method of evaluating the integral I the integral from a sub 1 to infinity ... the integral from a sub n to infinity of fx sub 1, x sub 2, ..., x sub n dx sub 1dx sub 2...dx sub n where fx sub 1, x sub 2, ..., x sub n is the joint multivariate normal density function with zero means and nonsingular variance-covariance matrix sigma through the combining of n k independent normal variables with zero means and unit variances. Later Marsaglia 1963 shows that this is a special case of a convolution formula. The complexity of implementing the solution is highly dependent upon the size of k and Marsaglia 1963 notes that k equal to n minus the multiplicity of the smallest latent root of sigma can always be achieved. This note investigates properties of sigma that will allow smaller values of k.
- Statistics and Probability