Hi,

When computing a tail probability for a bivariate Normal distribution, I noticed a strange behaviour. Specifically, say (X,Y) is normally distributed with mean (0,0) and variance (2,2) and covariance -0.5, and estimate Probability(X > 20 and Y > 20). The following three methods should return the same answer, however only the third method seems to work..

\[CapitalSigma] = {{2, -0.5}, {-0.5, 2}};
Dis = MultinormalDistribution[{0, 0}, \[CapitalSigma]];

Surv1[u_] := N[SurvivalFunction[Dis, {u, u}]];
Surv2[u_] := NProbability[X > u && Y > u, {X, Y} \[Distributed] Dis];
Surv3[u_] := NIntegrate[Boole[x > u && y > u]* PDF[Dis, {x, y}], {x, -\[Infinity], \[Infinity]}, {y, -\[Infinity], \[Infinity]}];

Surv1[20] (* Returns 2.36319 x 10^{-91}  *)
Surv2[20] (* Returns 0 *)
Surv3[20] (* Returns 7.08202 x 10^{-120} *)

Just wondering if anyone had an explanation for this :) As an aside, it seems that the first method performs better when the covariance becomes positive.

Thanks,

Pat Laub.