# Deltakl: Variance-Covariance Matrix of the Sample Membership... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

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

## Usage

 1 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

## Details

The klth unit of the Variance-Covariance matrix of the sample membership indicators is defined as Δ_{kl}=π_{kl}-π_kπ_l

## 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.

## Author(s)

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com

## 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.

VarHT, Pikl, Pik

## Examples

  1 2 3 4 5 6 7 8 9 10 11 # 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) 

### Example output

 1
[,1]    [,2]    [,3]    [,4]    [,5]
[1,]  0.2436 -0.0672 -0.0784 -0.0414 -0.0566
[2,] -0.0672  0.2244 -0.0132 -0.0722 -0.0718
[3,] -0.0784 -0.0132  0.2496 -0.0984 -0.0596
[4,] -0.0414 -0.0722 -0.0984  0.2211 -0.0091
[5,] -0.0566 -0.0718 -0.0596 -0.0091  0.1971


TeachingSampling documentation built on April 22, 2020, 1:05 a.m.