Poisson Sampling

Each unit is selected independently with its own inclusion probability. Sample size is random.

up_poisson(pik)

Arguments

pik

A numeric vector of inclusion probabilities between 0 and 1.

Value

An integer vector of selected indices. Length is random with expected value sum(pik).

Details

Poisson sampling is the simplest unequal probability method. Each unit k is selected independently with probability \(\pi_k\).

Properties:

• Random sample size with expectation \(\sum \pi_k\)

• Exact inclusion probabilities

• Independent selections

• Joint probabilities: \(\pi_{kl} = \pi_k \times \pi_l\)

See also

up_maxent() for fixed sample size maximum entropy sampling, bernoulli() for equal probability Bernoulli sampling

Examples

pik <- c(0.2, 0.5, 0.8, 0.3)

# Sample size varies
set.seed(42)
replicate(5, length(up_poisson(pik)))
#> [1] 4 2 3 3 2

# Expected size = sum(pik) = 1.8
mean(replicate(1000, length(up_poisson(pik))))
#> [1] 1.824