UPtillepi2 {sampling}

Joint inclusion probabilties for Tille sampling

Description

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

Usage

UPtillepi2(pik,eps=1e-6)

Arguments

pik

vector of the first-order inclusion probabilities.

eps

control value, by default equal to 1e-6.

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. The value eps is used to control pik (pik>eps & pik < 1-eps).

References

Tillé, Y. (1996), An elimination procedure of unequal probability sampling without replacement, Biometrika, 83:238-241.

See Also

UPtille

Examples

#defines the prescribed inclusion probabilities 
pik=c(0.2,0.7,0.8,0.5,0.4,0.4)
#matrix of joint inclusion probabilities  
UPtillepi2(pik)