# S.PPS: Probability Proportional to Size Sampling With Replacement In damarals/TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Draws a probability proportional to size sample with replacement of size m from a population of size N

## Usage

 `1` ```S.PPS(m,x) ```

## Arguments

 `m` Sample size `x` Vector of auxiliary information for each unit in the population

## Details

The selected sample is drawn according to the cumulative total method (sequential-list procedure)

## Value

The function returns a matrix of m rows and two columns. Each element of the first column indicates the unit that was selected. Each element of the second column indicates the selection probability of this unit

## 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.

`E.PPS`
 ``` 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``` ```############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Draws a PPS sample with replacement of size m=3 res <- S.PPS(3,x) sam <- res[,1] # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample according to a # PPS with replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income m <- 400 res<-S.PPS(400,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) ```