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In this paper, we consider the problem of improving the efficiency of a linear combination of two estimators when the population coefficient of variation is known. We generalized the discussion from the case of a parameter to a function of are interested parameter. We show that two estimators obtained from a improved linear combination of two estimators and a linear combination of two improved estimators are equivalent in terms of efficiency. We also show how a doubly-improved linear combination of two estimators can be constructed when the population coefficient of variation is known.

Improved Linear Combination of Two Estimators for a Function of Interested Parameter