Abstract
The well-known problem of unequal probability sampling of fixed size from a finite population can be generalised in a partitioning problem of a population into subsets, having unequal inlcusion probabilities in each subset. A simple algorithm that allows one to solve this problem is presented. The random partition of a population can be used to easily solve questions related to sample coordination in repeated sample surveys: the management of the overlap and the rotation. An application is developed where the maximal overlap of two samples selected with unequal probabilities is reached. Nevertheless, this method has an inconvenience: the samples must be selected at the same time. In order to overcome this difficulty, another method based on the multi-phase sampling method is also proposed.
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