The asymptotic unbiasedness and normality of alternative statistical estimators θ, θ,1··· of a given parameter θ* are generally proved without reference to any explicit knowledge of the exact finite sample distribution functions,Fn(x),Gn(x) ···. (Herendenotes sample size.) Within the class of asymptotically unbiased and normally distributed estimators of a given parameter it is sometimes possible to demonstrate that one estimator possesses a smaller asymptotic variance than another, or that one estimator possesses the smallest asymptotic variance within a particular subclass. Asymptotic theory obviously does not predict anything about finite sample distribution functionsFn(x), Gn(x) ···. In particular we cannot deduce from asymptotic theorems that the estimator with the smallest asymptotic variance will continue to exhibit the smallestdispersionin finite samples. Consequently it remains an essential task in positive estimation theory to derive the exact finite sample distribution functions of the alternative estimators that appear to be promising on the basis of asymptotic considerations.