Poisson sampling

In survey methodology, Poisson sampling (sometimes denoted as PO sampling^: 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.^: 85

Each element of the population may have a different probability of being included in the sample (${\displaystyle \pi _{i}}$). 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 (${\displaystyle p_{i}}$). 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.