# p.WR: Generalization of every with replacement sampling design In 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 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.

## 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) 

### Example output

Loading required package: dplyr

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

filter, lag

The following objects are masked from ‘package:base’:

intersect, setdiff, setequal, union

 1
 0.008 0.024 0.024 0.024 0.024 0.024 0.048 0.048 0.048 0.024 0.048 0.048
 0.024 0.048 0.024 0.008 0.024 0.024 0.024 0.024 0.048 0.048 0.024 0.048
 0.024 0.008 0.024 0.024 0.024 0.048 0.024 0.008 0.024 0.024 0.008
 1
 1
 0.002492952 0.007946285 0.010750856 0.020800569 0.008179999 0.008442927
 0.022845568 0.044201208 0.017382498 0.015454355 0.059801635 0.023517497
 0.057851582 0.045501244 0.008946874 0.002990203 0.012136708 0.023481892
 0.009234452 0.016420252 0.063539237 0.024987340 0.061467306 0.048345072
 0.009506053 0.007405212 0.042982425 0.016903201 0.083161649 0.065408038
 0.012861131 0.053633237 0.063275167 0.024883493 0.003261881
 1


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