UPsystematicpi2 {sampling}

Joint inclusion probabilities for systematic sampling

Description

Computes the joint (second-order) inclusion probabilities for systematic sampling.

Usage

UPsystematicpi2(pik)

Arguments

pik

vector of the first-order inclusion probabilities.

Value

Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size.

References

Madow, W.G. (1949), On the theory of systematic sampling, II, Annals of Mathematical Statistics, 20, 333-354.

See Also

UPsystematic

Examples

#define the prescribed inclusion probabilities
pik=c(0.2,0.7,0.8,0.5,0.4,0.4)
#matrix of joint inclusion probabilities
UPsystematicpi2(pik)