Identification of parameters by the distribution of the minimum: The tri-variate normal case with negative correlations

Let X 1 , X 2 , X 3 be a 3-variate normal vector with zero means and a non-singular co-variance matrix Σ , where for i ≠ j , Σ ij ≤ 0 . It is shown here that it is then possible to determine the three variances and the three correlations based only on the knowledge of the density of the minimum X 1 , X 2 , X 3 . Our method consists of careful determination and analysis of the asymptotic orders of various bivariate tail probabilities.