[Is there another name for these distributions?] If I take a Gaussian distribution with mean m and standard deviation s, then it would appear that integrate(pdf,x,m+6s,infinity) ~ 10^-9, so this upper tail integrates to 1 in a billion. Now suppose we want to form a "team" of k champions taken from this 6sigma tail. I should be able to convolve this distribution k times to get the pdf for the team. Is there a closed form for this pdf? How about simply the pdf for a pair of champions? I should be able to represent the 1-champion pdf as pdf_gaussian(x,m,s)*unit_step(x-(m+6*s))/tailintegral I'd like to laplace-transform this, exponentiate it k times, and then inverse transform it. Even if I can't find a closed form, I'd be interested in the mean & std of the k-champion distribution. Maxima seems to fail me. Does Mathematica do any better?