The main relations and differences between Poisson sampling and Bernoulli sampling

Poisson sampling It is a sampling process , Each element of the population has been subjected to an independent Bernoulli experiment , To determine if the element is part of the sample . Each element in the population may have a different probability of being included in the sample . If all first-order inclusions have equal probabilities , Then Poisson sampling is equivalent to Bernoulli sampling , Therefore, it can be considered as a special case of Poisson sampling .

Bernoulli sampling It is a sampling process , Each element of the population has been subjected to an independent Bernoulli experiment , To determine if the element is part of the sample . A basic characteristic of Bernoulli sampling is that all elements in the population have the same probability of being included in the sample . Therefore, Bernoulli sampling is a special case of Poisson sampling . In Poisson sampling , Each element of the population may have a different probability of being included in the sample . In Bernoulli sampling , All elements have equal probabilities . Because each element of the sample is considered separately , So the sample size is not fixed , It follows a binomial distribution .