A MODEL OF SYSTEMATIC SAMPLING WITH UNEQUAL PROBABILITIES

A new method is described of drawing, without replacement, two sample units per stratum from any population. The method is developed from a consideration of the asymptotic properties of systematic sampling with unequal probabilities, as the sizes of the population units tend to zero. The essential properties of this method are very easily analysed. They also converge, over a large number of strata, to those of systematic sampling from the same strata with their population units arranged in random order. In proving this, the assumption is made that the underlying population is of the type to which it is appropriate to apply ratio estimation. The sampling method described is, however, simple enough to commend itself as an alternative to systematic sampling when the underlying population is not of this type. Consideration is given to the case where the sizes of some of the population units exceed the skip interval.