[EMAIL PROTECTED] (David) wrote in message news:<[EMAIL PROTECTED]>... > Thanks in advance for any time spent helping me with this one: > A, B and C are 3 Normally distributed variables with known parameters. > Does anyone know of method(s) to determine the probability of A > beating B and C in a 3 man field? I am hoping to find an analytical > solution, but other suggestions would be welcome also. > Thanks again
I assume that you mean (A,B,C) is trivariate normal, with known mean vector and covariance matrix. Let X = A-B and Y = A-C. Then (X,Y) is bivariate normal with known mean vector and covariance matrix, and your question is "What is the probability of observing (X > 0, Y > 0)?". Let u = Mean(X)/SD(X), v = Mean(Y)/SD(Y), w = Cov(X,Y)/(SD(X)SD(Y)). Let F(z) denote the standard normal cdf, and let f(x,y,r) denote the bivariate standard normal pdf. Then Pearson (~1901) showed that your desired probability is Integral_0^w f(u,v,r)dr + F(u)F(v). . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
