Survey Methodology
Unequal probability inverse sampling

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by Yves TilléNote 1

  • Release date: December 20, 2016


In an economic survey of a sample of enterprises, occupations are randomly selected from a list until a number r of occupations in a local unit has been identified. This is an inverse sampling problem for which we are proposing a few solutions. Simple designs with and without replacement are processed using negative binomial distributions and negative hypergeometric distributions. We also propose estimators for when the units are selected with unequal probabilities, with or without replacement.

Key Words: Location; Horvitz-Thompson estimator; Negative binomial; Negative hypergeometric; Inverse design; Inclusion probability; Wage.

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How to cite

Tillé, Y. (2016). Unequal probability inverse sampling. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 42, No. 2. Paper available at


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