Independent observations X0, X1…, XN+1 are drawn from each of N populations whose distribution functions F(x – θi) have means θ i, 0 ≦ i < N, and we wish to calculate the probability Pk;N that X0 is the k th largest observation. For normal populations an approximation is given for PK;N based on a Taylor series expansion in the θ 's. If F(x) has an increasing failure rate, as is the case for the normal, an upper bound can be given for the ‘win' probability P1;N Some moment relations for normal order statistics are also given.
