TeachingSampling (version 4.1.1)

Deltakl: Variance-Covariance Matrix of the Sample Membership Indicators for Fixed Size Without Replacement Sampling Designs

Description

Computes the Variance-Covariance matrix of the sample membership indicators in the population given a fixed sample size design

Usage

Deltakl(N, n, p)

Arguments

N

Population size

n

Sample size

p

A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one

Value

The function returns a symmetric matrix of size \(N \times N\) containing the variances-covariances among the sample membership indicators for each pair of units in the finite population.

Details

The \(kl\)th unit of the Variance-Covariance matrix of the sample membership indicators is defined as \(\Delta_{kl}=\pi_{kl}-\pi_k\pi_l\)

References

Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer. Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.

See Also

VarHT, Pikl, Pik

Examples

# NOT RUN {
# Vector U contains the label of a population of size N=5
U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie")
N <- length(U)
# The sample size is n=2
n <- 2
# p is the probability of selection of every sample. 
p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08)
# Note that the sum of the elements of this vector is one
sum(p)
# Computation of the Variance-Covariance matrix of the sample membership indicators
Deltakl(N, n, p)
# }