Originally Posted by

**daaaaave** Ok, so let me try to explain fully what I'm attempting to do.

I am assuming there are N normal random variables with parameters X (mean) and Var. Let's say we take 1 observation from 2 of these random variables at a time and are told which RV was greater but not their value. Then, I believe the likelihood function is:

f(Q | X, Var) = the product of P(A > B) where A is the sample from which the greater observation was drawn

The data (Q) just tells us if we are using P(A > B) or P(B > A) in the likelihood function for that observation.

Then, I take the log and try to maximize with respect to the parameters (X, Var) for each random variable (A, B, .....). Since P(A > B) is just a standard normal difference CDF, I am taking the derivative of that.

Does that make sense?