A NOTE ON THE EVALUATION OF A MULTIVARIATE NORMAL INTEGRAL BY THE METHOD OF DAS
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 f(x sub 1, x sub 2, ..., x sub n) (dx sub 1)(dx sub 2)...(dx sub n) (where f(x 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 03, 1968
- Accession Number
- AD0680437
Entities
People
- J. T. Webster
Organizations
- Southern Methodist University