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

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

1 | ```
Pik(p, Ind)
``` |

`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 |

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 *π_k* and obtained from a given sampling design as follows:

*π_k=∑_{s\ni k}p(s)*

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

Hugo Andres Gutierrez Rojas hugogutierrez@usantotomas.edu.co

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# 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)
``` |

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