Sampling with probabilities proportional to the variable of interest

J.J.A. Moors, R. Smeets, F.W.M. Boekema

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To estimate the mean sojourn time, a sample of Tilburg fair visitors was asked for the duration of their stay on the fair grounds. The longer a visitor's sojourn, the larger his/her probability of being interviewed will be; therefore, longer sojourn times will be overrepresented in the sample. As a consequence, the arithmetic sample mean is not a suitable estimator. The paper places this problem against a theoretical background. As a better estimator the harmonic mean of the observed sojourn times is presented. In addition, a variance estimator is given. The properties of these estimators are difficult to derive analytically. Instead, their behaviour is studied in a number of examples.
Original languageEnglish
PublisherUnknown Publisher
Number of pages15
VolumeFEW 717
Publication statusPublished - 1996

Publication series

NameResearch memorandum / Tilburg University, Faculty of Economics and Business Administration
VolumeFEW 717


  • Probability
  • Estimation
  • Sampling
  • statistics


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