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Research article - Peer-reviewed, 2012

Size constrained unequal probability sampling with a non-integer sum of inclusion probabilities

Grafström, Anton; Qualité, Lionel; Tillé, Yves; Matei, Alina


More than 50 methods have been developed to draw unequal probability samples with fixed sample size. All these methods require the sum of the inclusion probabilities to be an integer number. There are cases, however, where the sum of desired inclusion probabilities is not an integer. Then, classical algorithms for drawing samples cannot be directly applied. We present two methods to overcome the problem of sample selection with unequal inclusion probabilities when their sum is not an integer and the sample size cannot be fixed. The first one consists in splitting the inclusion probability vector. The second method is based on extending the population with a phantom unit. For both methods the sample size is almost fixed, and equal to the integer part of the sum of the inclusion probabilities or this integer plus one.


Survey sampling; maximum entropy; splitting method

Published in

Electronic Journal of Statistics
2012, volume: 6, pages: 1477-1489

Authors' information

Swedish University of Agricultural Sciences, Department of Forest Resource Management
Qualité, Lionel
University of Neuchâtel
Tillé, Yves
University of Neuchâtel
Matei, Alina
University of Neuchâtel

UKÄ Subject classification

Probability Theory and Statistics

Publication Identifiers


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