South Florida Business Daily

What is the expected value of a truncated trivariate normal distribution?

Specifically, if x, y, and z have a trivariate normal distribution, I am interested in E[x|y>a,z=b] and VAR[x|y>a,z=b] if a and b are constants. I have the formula for E[x|y>a] and E[x|y=a] for a bivariate normal distribution and was hoping there was an equally straightforward formula for the trivariate case.

Public Comments

1. It's not going to be equally straightforward since you're effectively increasing your arguments by an exponent. You can derive the formula, but it'd be a nightmare and take you almost as long as workign through it the hard way yourself. Try Hogg and Tanis for a proof.