Comparison Of Some Methods In Unequal Probability Sampling

Sampling with unequal probabilities is an important sampling technique and very popular in practice.First, this paper gives an introduction of some methods of unequal probability sampling, their estimators and variance estimators, including sampling with pps with replacement, methods of sampling without replacement suggested by Brewer, Durbin, Sampford , Des Raj , Murthy , Rao-Hartley-Cochran.Then, at the basis of Rao and Bayless's study , we consider that population can be splited two random subpopulations, which are respectively drawn from different infinite super-populations, and compare the stabilities of estimators of the methods that given above. We find that the minor difference between two super-populations has great effect on the efficiency of the estimators for the population with moderately large coefficient of variation (C.V.).