SunterSampling (version 1.0.1)

sunterpi: Inclusion probabilities for Sunter sampling

Description

The function computes the inclusion probabilities for Sunter sampling.

Usage

sunterpi(x, n)

Arguments

x

the vector of values of the auxiliary variable (measure of size)

n

the sample size

Value

a vector that contains the first-order inclusion probabilities for each unit $k$ in the population; $N$ is the population size.

Details

Citing the reference, "For the most part of the population, Sunter's scheme gives the inclusion probability $\pi_k$ strictly proportional to $x_k$. For a small portion of the population, corresponding to the elements with the smallest $x_k$-values, equal, rather than $x_k$-proportional, inclusion probability is applied to gain simplicity."

References

C-E. Sarndal, B. Swensson, J. Wretman: Model Assisted Survey Sampling, Springer, New York, 1992

See Also

sunter, sunterpi2

Examples

# Ex.1 from Sarndal et al. (1992)
x<-c(40,25,20,10,5)
n<-2
sunterpi(x,n)
# note that the inclusion probabilities are not exactly proportional
# to the measures of size
n*x/sum(x)

# Ex.2
# set the population size
N<-100
set.seed(1)
# build a vector of measures of size
x<-rnorm(N,100,25)
sort(x)
# set the sample size
n<-10
# inclusion probabilities for Sunter's sampling
pi<-sunterpi(x,n)
pi
# theoretical inclusion probabilities
pik<-n*x/sum(x)
pik
# note the difference between actual and theoretical inclusion probabilities
sort(pi)
sort(pik)