In
survey methodology
Survey methodology is "the study of survey methods".
As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey ...
, Poisson sampling (sometimes denoted as ''PO sampling''
) is a
sampling process where each element of the
population
Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using ...
is subjected to an
independent
Independent or Independents may refer to:
Arts, entertainment, and media Artist groups
* Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s
* Independe ...
Bernoulli trial
In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is ...
which determines whether the element becomes part of the sample.
[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)
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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 In the theory of finite population sampling, Bernoulli sampling 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. An essential p ...
, which can therefore be considered to be a special case of Poisson sampling.
A mathematical consequence of Poisson sampling
Mathematically, the first-order inclusion probability of the ''i''th element of the population is denoted by the symbol π''i'' and the second-order inclusion probability that a pair consis