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Poisson sampling

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In survey methodology, Poisson sampling (sometimes denoted as PO sampling[1]: 61 ) is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample.[1]: 85 [2]

Each element of the population may have a different probability of being included in the sample (). The probability of being included in a sample during the drawing of a single sample is denoted as the first-order inclusion probability of that element (). If all first-order inclusion probabilities are equal, Poisson sampling becomes equivalent to Bernoulli sampling, which can therefore be considered to be a special case of Poisson sampling.

A mathematical consequence of Poisson sampling

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Mathematically, the first-order inclusion probability of the ith element of the population is denoted by the symbol and the second-order inclusion probability that a pair consisting of the ith and jth element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by .

The following relation is valid during Poisson sampling when :

is defined to be .

See also

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References

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  1. ^ a b Carl-Erik Sarndal; Bengt Swensson; Jan Wretman (1992). Model Assisted Survey Sampling. ISBN 978-0-387-97528-3.
  2. ^ Ghosh, Dhiren, and Andrew Vogt. "Sampling methods related to Bernoulli and Poisson Sampling." Proceedings of the Joint Statistical Meetings. American Statistical Association Alexandria, VA, 2002. (pdf)