6. Unequal Probability Sampling

  1. Steven K. Thompson

Published Online: 10 FEB 2012

DOI: 10.1002/9781118162934.ch6

Sampling, Third Edition

Sampling, Third Edition

How to Cite

Thompson, S. K. (2012) Unequal Probability Sampling, in Sampling, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118162934.ch6

Author Information

  1. Simon Fraser University, Canada

Publication History

  1. Published Online: 10 FEB 2012
  2. Published Print: 23 FEB 2012

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470402313

Online ISBN: 9781118162934



  • generalized unequal-probability estimator;
  • Hansen–Hurwitz estimator;
  • Horvitz–Thompson estimator;
  • unequal probability sampling


With some sampling procedures, different units in the population have different probabilities of being included in a sample. The differing inclusion probabilities may result from some inherent feature of the sampling procedure, or they may be imposed deliberately to obtain better estimates by including “more important” units with higher probability. In either case, the unequal inclusion probabilities must be taken into account in order to come up with reasonable estimates of population quantities. This chapter first discusses Hansen–Hurwitz estimator and Horvitz–Thompson estimator. It then describes generalized unequal-probability estimator. Finally, the chapter presents some R code for selecting samples with unequal probability replacement and computing Hansen–Hurwitz and Horvitz–Thompson estimates.

Controlled Vocabulary Terms

estimator; probability sampling