Graduation Year

2007

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Mathematics and Statistics

Major Professor

Arunava Mukherjea, Ph.D.

Keywords

Tri-variate normal, Parameter identification, Minimum variate, Asymptotic order, Tail probabilities

Abstract

Let (X1,X2,X3) be a tri-variate normal vector with a non-singular co-variance matrix, and where each covariance is negative. It is shown here that it is then possible to determine the three means, the three variances and the three correlation coefficients based only on the knowledge of the probability density function for the minimum variate. We will present a method for identifying the nine parameters which consists of careful determination of the asymptotic orders of various bivariate tail probabilities.

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