# 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