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A Class of Sampling Two Units with Probability Proportional to Size
Authors:Jehad Al-jararha
Institution:Department of Statistics , Yarmouk University , Irbid , Jordan
Abstract:A class of sampling two units without replacement with inclusion probability proportional to size is proposed in this article. Many different well known probability proportional to size sampling designs are special cases from this class. The first and second inclusion probabilities of this class satisfy important properties and provide a non-negative variance estimator of the Horvitz and Thompson estimator for the population total. Suitable choice for the first and second inclusion probabilities from this class can be used to reduce the variance estimator of the Horvitz and Thompson estimator. Comparisons between different proportional to size sampling designs through real data and artificial examples are given. Examples show that the minimum variance of the Horvitz and Thompson estimator obtained from the proposed design is not attainable for the most cases at any of the well known designs.
Keywords:First- and second-ordered inclusion probabilities  Horvitz and Thompson estimator  Probability proportional to size sampling designs
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