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Controlled Probability Proportional to Size Sampling Designs.
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF MATHEMATICS
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Any sampling design, d, of size n without replacement based on a finite population u of N units or strata can be formally presented by a pair s sub d, P sub d, where S sub d called the support of d is any set of subsets of size n each based on the elements of u such that the set theoretic union of these subsets, called samples, is u and P sub d is a strictly positive probability distribution on S sub d. A sampling design is said to be a probability proportional to size, denoted by PPSN,n, if the probability that the unit i is being selected in a random sample is proportional to a known positive quantity associated with the unit i 1,2,...,N. The literature of survey sampling offers a PPSN,n with S sub d consists of all N over n possible samples. Here we give an easily applicable technique for the construction of PPSN,n with various support sizes and various probabilities on each support. Such sampling designs are needed for controlled samplings when some samples are undesirable to be chosen or we need to minimize or maximize the probabilities of the selection of certain samples. Author
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