Poisson sampling

Mathematically, the first-order inclusion probability of the ith element of the population is denoted by the symbol ${\displaystyle \pi _{i}}$ 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 ${\displaystyle \pi _{ij}}$.

The following relation is valid during Poisson sampling when ${\displaystyle i\neq j}$:

${\displaystyle \pi _{ij}=\pi _{i}\times \pi _{j}.}$

${\displaystyle \pi _{ii}}$ is defined to be ${\displaystyle \pi _{i}}$.

• Bernoulli sampling
• Poisson distribution
• Poisson process
• Sampling design