TeachingSampling (version 4.1.1)

Pik: Inclusion Probabilities for Fixed Size Without Replacement Sampling Designs

Description

Computes the first-order inclusion probability of each unit in the population given a fixed sample size design

Usage

Pik(p, Ind)

Arguments

p

A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one

Ind

A sample membership indicator matrix

Value

The function returns a vector of inclusion probabilities for each unit in the finite population.

Details

The inclusion probability of the \(k\)th unit is defined as the probability that this unit will be included in a sample, it is denoted by \(\pi_k\) and obtained from a given sampling design as follows: $$\pi_k=\sum_{s\ni k}p(s)$$

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.

See Also

HT

Examples

# NOT RUN {
# Vector U contains the label of a population of size N=5
U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie")
N <- length(U)
# The sample size is n=2
n <- 2
# The sample membership matrix for fixed size without replacement sampling designs
Ind <- Ik(N,n)
# p is the probability of selection of every sample. 
p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08)
# Note that the sum of the elements of this vector is one
sum(p)
# Computation of the inclusion probabilities
inclusion <- Pik(p, Ind)
inclusion
# The sum of inclusion probabilities is equal to the sample size n=2
sum(inclusion)
# }