Some Easily Found Minimum Variance Unbiased Estimators

Several methods are available for finding minimum variance unbiased estimators for functions of distribution parameters.This paper concentrates on two which are rarely used but simple when applicable.The first, previously discussed by Davis (1951) and Tate (1959), yields estimators by differentiation when the range of nonzero probability for a continuous random variable depends on an unknown parameter.The second, which has wider applicability, permits estimators for some rather complicated functions to be found by using some well-known results from distribution theory.A number of examples are presented, many of which are suitable for classroom exercises.