Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 |

`N` |
Population size |

`Pik` |
Vector of inclusion probabilities for each unit in the population |

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.

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.

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com

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.

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)[1]
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)
``` |

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