Horvitz andThompson  considered varying probability sampling method in general and furnished an unbiased estimator of the population total.Rao, Hartley andCochran  proposed a simple procedure of unequal probability sampling with replacement. It leads to an estimator of the population total having smaller variance than is obtained by sampling with replacement. An attempt has been made in the present paper to compare efficiencies ofHorvitz-Thompson's estimator with that due toRao, hartley andCochran. It is demonstrated that the generalized πps sampling strategy consisting of the design with π i , the probability of inclusion of thei-th population unit in the sample proportional to the modified size together withHorvitz-Thompson's estimator is superior toRao, Hartley andCochran's sampling strategy under a general super-population model.
KeywordsStochastic Process Population Total Sampling Method Probability Theory Economic Theory
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