# Pik: Inclusion Probabilities for Fixed Size Without Replacement... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

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

## Usage

 `1` ```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

## Details

The inclusion probability of the kth 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)

## Value

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

## Author(s)

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com

## 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.

`HT`

## Examples

 ``` 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) ```

### Example output

```[1] 1
[,1] [,2] [,3] [,4] [,5]
[1,] 0.58 0.34 0.48 0.33 0.27
[1] 2
```

TeachingSampling documentation built on April 22, 2020, 1:05 a.m.