Poisson sampling

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.

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