Summary
The question of the existence of a sampling design realizing given preassigned inclusion probabilities is treated. The question can be fully answered in the case of inclusion probabilities of first order. If the inclusion probabilities of second order are given it is shown why necessary and sufficient conditions for the existence of a corresponding sampling design can be derived only in very special cases.
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Gabler, S., Schweigkoffer, R. The existence of sampling designs with preassigned inclusion probabilities. Metrika 37, 87–96 (1990). https://doi.org/10.1007/BF02613510
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DOI: https://doi.org/10.1007/BF02613510