Modified probability proportional to size sampling

ABSTRACT

Probability proportional to size (PPS) sampling is one of the most widely used designs for finite populations. We propose modifications to PPS designs with replacement and Rao–Hartley–Cochran design without replacement. These modifications consist of division of the population into two groups. Units in the first group are included in the sample with probability one. Under certain conditions, in both with and without replacement designs, the estimator of the population total based on the modified PPS sampling design is shown to be better than the corresponding estimator based on a PPS design. We illustrate our modification by an example and an application.

KEYWORDS:

• Probability proportional to size
• Rao–Hartley–Cochran sampling design
• With replacement sampling
• Without replacement sampling
• Zipf’s law

MATHEMATICS SUBJECT CLASSIFICATION:

• 62-xx
• 62D05

Acknowledgments

We thank the reviewer of the paper for constructive criticism and a number of useful suggestions.