Accession Number : ADA119368

Title :   On the Evaluation of Certain Multivariate Normal Probabilities.

Descriptive Note : Technical rept.,


Personal Author(s) : Iyengar,Satish

PDF Url : ADA119368

Report Date : 12 Aug 1982

Pagination or Media Count : 81

Abstract : Consider the following problem: if X is an n-dimensional normally distributed random vector with mean zero and covariance matrix evaluate the probability, pk, that k components of X exceed a given constant. We call (po,...,pn) the exceedance distribution and study its behavior as the covariance matrix varies. The pk's can be expressed as multidimensional integrals; these expressions, however, are not helpful, for simulation and numerical intergration in high dimensions are very expensive. When covariance is an equicorrelation matrix or has single-factor structure, the probabilities can be written as single integrals. In this dissertation, we propose some methods for approximating the above multidimensional integrals by such single integrals. Ample numerical evidence is given to show that the approximations are quite good. We also prove theorem which gives conditions for the variance of the exceedance distribution to be greater than that of the approximation. We use this inequality to improve upon earlier approximations and inequalities.

Descriptors :   *Multivariate analysis, *Probability distribution functions, *Normalizing(Statistics), Approximation(Mathematics), Normal density functions, Numerical analysis, Covariance, Matrices(Mathematics), Asymptotic normality, Statistical inference, Analysis of variance, Inequalities

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE