Probability-proportional-to-size sampling

In survey methodology, probability-proportional-to-size (pps) sampling is a sampling process where each element of the population (of size N) has some (independent) chance p i {\displaystyle p_{i}} to be selected to the sample when performing one draw. This p i {\displaystyle p_{i}} is proportional to some known quantity x i {\displaystyle x_{i}} so that p i = x i ∑ i = 1 N x i {\displaystyle p_{i}={\frac {x_{i}}{\sum _{i=1}^{N}x_{i}}}} .

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