# Pikl: Second Order Inclusion Probabilities for Fixed Size Without... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the second-order inclusion probabilities of each par of units in the population given a fixed sample size design

## Usage

 1 Pikl(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 second-order inclusion probability of the klth units is defined as the probability that unit k and unit l will be both included in a sample; it is denoted by π_{kl} and obtained from a given sampling design as follows:

π_{kl}=∑_{s\ni k,l}p(s)

## Value

The function returns a symmetric matrix of size N \times N containing the second-order inclusion probabilities 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, Deltakl, 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 second-order inclusion probabilities Pikl(N, n, p) 

### Example output

[1] 1
[,1] [,2] [,3] [,4] [,5]
[1,] 0.58 0.13 0.20 0.15 0.10
[2,] 0.13 0.34 0.15 0.04 0.02
[3,] 0.20 0.15 0.48 0.06 0.07
[4,] 0.15 0.04 0.06 0.33 0.08
[5,] 0.10 0.02 0.07 0.08 0.27


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