UPmidzunopi2 {sampling}

Joint inclusion probabilities for Midzuno sampling

Description

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

Usage

UPmidzunopi2(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

Midzuno, H. (1952), On the sampling system with probability proportional to sum of size. Annals of the Institute of Statistical Mathematics, 3:99-107.

See Also

UPmidzuno

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
UPmidzunopi2(pik)