Accession Number:
AD0680437
Title:
A NOTE ON THE EVALUATION OF A MULTIVARIATE NORMAL INTEGRAL BY THE METHOD OF DAS
Descriptive Note:
Technical rept.
Corporate Author:
SOUTHERN METHODIST UNIV DALLAS TX DEPT OF STATISTICAL SCIENCE
Personal Author(s):
Report Date:
1968-12-03
Pagination or Media Count:
8.0
Abstract:
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.
Descriptors:
Subject Categories:
- Statistics and Probability