Joint Inclusion Probabilities for Poisson Sampling

Computes joint inclusion probabilities for Poisson sampling. Since selections are independent, \(\pi_{ij} = \pi_i \times \pi_j\).

up_poisson_jip(pik)

Arguments

pik

numeric vector of first-order inclusion probabilities.

Value

A symmetric N×N matrix of joint inclusion probabilities.

Details

For Poisson sampling, units are selected independently, so: $$\pi_{ij} = \pi_i \pi_j \quad \text{for } i \neq j$$

Examples

pik <- c(0.2, 0.5, 0.8)
pikl <- up_poisson_jip(pik)