How to compute lower tail probability for the Bivariate Normal Distribution

G'day,

I am trying to compute the lower tail probability for the bivariate Normal distribution given by the following formula for 2 random variables (X1, X2):

Where X1 = -1.23, X2 = -2.75 and rho = 0.65. I am very curious how to solve this problem?

The first term it's just calculations but how would you attack the integrals?

Can someone provide me with some code or hints or if it's possible a solution? X's are log normal distributed random variables.

Furthermore; how would extend it to multiple dimensions. If we say we have a variable X_3 = -1.78. How would you attack that?

Answer 1

[Jeff Miller]

The function 'mvncdf' computes the lower tail probability for the multivariate normal distribution.