TeachingSampling (version 4.1.1)

S.PO: Poisson Sampling

Description

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

Usage

S.PO(N, Pik)

Arguments

N

Population size

Pik

Vector of inclusion probabilities for each unit in the population

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.

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.

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.

See Also

E.PO

Examples

# NOT RUN {
############
## 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)
# }