# S.PO: Poisson Sampling In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Draws a Poisson sample of expected size \$n\$ from a population of size \$N\$

## Usage

 `1` ```S.PO(N, Pik) ```

## Arguments

 `N` Population size `Pik` Vector of inclusion probabilities for each unit in the population

## Details

The selected sample is drawn according to a sequential procedure algorithm based on a uniform distribution. The Poisson sampling design is not a fixed sample size one.

## Value

The function returns a vector of size N. Each element of this vector indicates if the unit was selected. Then, if the value of this vector for unit k is zero, the unit k was not selected in the sample; otherwise, the unit was selected in the 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.
Tille, Y. (2006), Sampling Algorithms. Springer.

`E.PO`
 ``` 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``` ```############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Draws a Bernoulli sample without replacement of expected size n=3 # "Erik" is drawn in every possible sample becuse its inclusion probability is one Pik <- c(0.5, 0.2, 1, 0.9, 0.5) sam <- S.PO(5,Pik) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a Poisson sample data(Lucy) attach(Lucy) N <- dim(Lucy) n <- 400 Pik<-n*Income/sum(Income) # None element of Pik bigger than one which(Pik>1) # The selected sample sam <- S.PO(N,Pik) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) ```