Abstract
Abstract In this paper a new set of revised probabilities are proposed under Midzuno, 1950 , Ann. Inst. Statist. Math., vol. 1, pp. 149 –156 sampling scheme. The revised probabilities are functions of location shift factor L, with values between zero and unity. This modification gives rise to a class of Horvitz and Thompson, 1952 , J. Am. Statist. Assoc., vol. 47, pp. 663– 685, H–T estimators for different choices of L. Under a super population model Chromy (1974) a suitable choice of L is provided by minimizing the expected variance under the model. The choice of L does not need the knowledge of any unknown population parameters. It is shown that the suggested scheme is far less restrictive. An illustration is given using hypothetical as well as natural populations.
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