# E.PPS: Estimation of the Population Total under Probability... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the Hansen-Hurwitz estimator of the population total according to a probability proportional to size sampling with replacement design

## Usage

 `1` ```E.PPS(y, pk) ```

## Arguments

 `y` Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample `pk` A vector containing selection probabilities for each unit in the sample

## Details

Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation estimated under a probability proportional to size sampling with replacement design

## Value

The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest

## 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.

`S.PPS, HH`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# Uses the Lucy data to draw a random sample according to a # PPS with replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income m <- 400 res <- S.PPS(m,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # pk.s is the selection probability of each unit in the selected sample pk.s <- res[,2] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.PPS(estima,pk.s) ```

### Example output

```The following objects are masked from Lucy:

Employees, ID, Income, Level, SPAM, Taxes, Ubication, Zone

 "ID"        "Ubication" "Level"     "Zone"      "Income"    "Employees"
 "Taxes"     "SPAM"
N       Income    Employees        Taxes
Estimation     2263.467025 1.035217e+06 1.502993e+05 3.017928e+04
Standard Error   78.308762 2.540391e-12 4.624637e+03 9.132950e+02
CVE               3.459682 2.453969e-16 3.076951e+00 3.026232e+00
DEFF                   Inf 5.184543e-33 1.243090e+00 8.050351e-02
```

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