Joint Inclusion Probabilities for Systematic Sampling

Computes exact joint inclusion probabilities for systematic sampling with unequal probabilities.

up_systematic_jip(pik, eps = 1e-06)

Arguments

pik

numeric vector of first-order inclusion probabilities.

eps

tolerance for boundary detection (default 1e-6).

Value

A symmetric N×N matrix of joint inclusion probabilities.

Note

Systematic sampling is NOT a high-entropy design. Many joint probabilities will be exactly zero.

References

Tillé, Y. (2006). Sampling Algorithms. Springer.

Examples

pik <- c(0.2, 0.3, 0.5)
pikl <- up_systematic_jip(pik)