# PikSTPPS: Inclusion Probabilities in Stratified Proportional to Size... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

For a given sample size, in each stratum, this function returns a vector of first order inclusion probabilities for an stratified sampling design proportional to an auxiliary variable.

## Usage

 `1` ```PikSTPPS(S, x, nh) ```

## Arguments

 `S` Vector identifying the membership to the strata of each unit in the population. `x` Vector of auxiliary information for each unit in the population. `nh` The vector defningn the sample size in each stratum.

## Details

is not always less than unity. A sequential algorithm must be used in order to ensure that for every unit in the population the inclusion probability gives a proper value; i.e. less or equal to unity.

## Value

A vector of inclusion probablilities in a stratified finite population.

## Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

## References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas Sarndal, C-E. and Swensson, B. and Wretman, J. (2003), Model Assisted Survey Sampling. Springer.

`PikHol, PikPPS, S.STpiPS`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52``` ```############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # The sample size in each stratum nh <- c(2,2) # The vector of inclusion probablities for a stratified piPS sample # without replacement of size two within each stratum Pik <- PikSTPPS(Strata, x, nh) Pik # Some checks sum(Pik) sum(nh) ############ ## Example 2 ############ # Uses the Lucy data to compute the vector of inclusion probablities # for a stratified random sample according to a piPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 # Defines the sample size at each stratum n1<-70 n2<-100 n3<-200 nh<-c(n1,n2,n3) nh # Computes the inclusion probabilities for the stratified population S <- Level x <- Employees Pik <- PikSTPPS(S, x, nh) # Some checks sum(Pik) sum(nh) ```

### Example output

```Loading required package: dplyr

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

filter, lag

The following objects are masked from ‘package:base’:

intersect, setdiff, setequal, union

[,1]
[1,] 0.5561497
[2,] 0.6417112
[3,] 0.8021390
[4,] 1.0000000
[5,] 1.0000000
[1] 4
[1] 4
Big Medium  Small
83    737   1576
[1] 83
[1] 737
[1] 1576
[1]  70 100 200
[1] 370
[1] 370
```

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