# S.BE: Bernoulli Sampling Without Replacement In damarals/TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Draws a Bernoulli sample without replacement of expected size \$n\$ from a population of size \$N\$

## Usage

 `1` ```S.BE(N, prob) ```

## Arguments

 `N` Population size `prob` Inclusion probability for each unit in the population

## Details

The selected sample is drawn according to a sequential procedure algorithm based on an uniform distribution. The Bernoulli 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 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.
Tille, Y. (2006), Sampling Algorithms. Springer.

`E.BE`
 ``` 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``` ```############ ## 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 # The inlusion probability is 0.6 for each unit in the population sam <- S.BE(5,0.6) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a Bernoulli sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population size is 2396. If the expected sample size is 400 # then, the inclusion probability must be 400/2396=0.1669 sam <- S.BE(N,0.01669) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) ```