On Successive Sampling and Fixed Inclusion Probabilities

In the method of successive sampling, a sample of n distinct units is drawn from a population of N units one at a time. Each unit i is drawn with a fixed selection probability pi and any repeated units are ignored. When the pi are proportional to a given size measure, this is called probability proportional to size without replacement (PPSWOR). The first order inclusion probabilities πi of each unit in a PPSWOR scheme are not proportional to the size measure, as proved in Kochar and Korwar (2001). This article discusses a modification to the selection probabilities which creates a successive sampling scheme where first order inclusion probabilities are proportional to size (IPPS) in the case when n = 2.