# OrderWR: Pseudo-Support for Fixed Size With Replacement Sampling... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Creates a matrix containing every possible ordered sample under fixed sample size with replacement designs

## Usage

 `1` ```OrderWR(N,m,ID=FALSE) ```

## Arguments

 `N` Population size `m` Sample size `ID` By default FALSE, a vector of values (numeric or string) identifying each unit in the population

## Details

The number of samples in a with replacement support is not equal to the number of ordered samples induced by a with replacement sampling design.

## Value

The function returns a matrix of N^m rows and m columns. Each row of this matrix corresponds to a possible ordered sample.

## Author(s)

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com. The author acknowledges to Hanwen Zhang for valuable suggestions.

## References

Tille, Y. (2006), Sampling Algorithms. Springer
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

`SupportWR, Support`
 ``` 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``` ```# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # Under this context, there are five (5) possible ordered samples OrderWR(N,1) # The same output, but labeled OrderWR(N,1,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) OrderWR(N,1,ID=y) # If the smaple size is m=2, there are (25) possible ordered samples OrderWR(N,2) # The same output, but labeled OrderWR(N,2,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) OrderWR(N,2,ID=y) # Note that the number of ordered samples is not equal to the number of # samples in a well defined with-replacement support OrderWR(N,2) SupportWR(N,2) OrderWR(N,4) SupportWR(N,4) ```