ABSTRACT
The sampling units of unequal size are selected by probabilities proportional to their size (pps). Sampling units can be selected with pps with or without replacement. This distinction is immaterial for infinite populations, as in sampling points from an area. pps sampling with replacement (ppswr) is much easier to implement than pps sampling without replacement (ppswor). In ppswor sampling the inclusion probabilities are proportional to a size variable, not the draw-by-draw selection probabilities as in ppswr. ppswor sampling starts with assigning target inclusion probabilities to all units in the population. A simple, straightforward method is systematic ppswor sampling. Two subtypes can be distinguished, systematic ppswor sampling with fixed frame order and systematic ppswor sampling with random frame order. Given some order of the units, the cumulative sum of the inclusion probabilities is computed. Another interesting algorithm for ppswor sampling is the pivotal method.
