# p.WR: Generalization of every with replacement sampling design In damarals/TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the selection probability (sampling design) of each with replacement sample

## Usage

 1 p.WR(N, m, pk) 

## Arguments

 N Population size m Sample size pk A vector containing selection probabilities for each unit in the population

## Details

Every with replacement sampling design is a particular case of a multinomial distribution.

p(\mathbf{S}=\mathbf{s})=\frac{m!}{n_1!n_2!\cdots n_N!}∏_{i=1}^N p_k^{n_k}

where n_k is the number of times that the k-th unit is selected in a sample.

## Value

The function returns a vector of selection probabilities for every with-replacement sample.

## Author(s)

Hugo Andres Gutierrez Rojas hugogutierrez@usantotomas.edu.co

## 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.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ############ ## Example 1 ############ # With replacement simple random sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector pk is the sel?ection probability of the units in the finite population pk <- c(0.2, 0.2, 0.2, 0.2, 0.2) sum(pk) N <- length(pk) m <- 3 # The smapling design p <- p.WR(N, m, pk) p sum(p) ############ ## Example 2 ############ # With replacement PPS random sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector x is the auxiliary information and y is the variables of interest x<-c(32, 34, 46, 89, 35) y<-c(52, 60, 75, 100, 50) # Vector pk is the sel?ection probability of the units in the finite population pk <- x/sum(x) sum(pk) N <- length(pk) m <- 3 # The smapling design p <- p.WR(N, m, pk) p sum(p) 

damarals/TeachingSampling documentation built on June 2, 2019, 9:06 p.m.