# E.PO: Estimation of the Population Total under Poisson Sampling... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the Horvitz-Thompson estimator of the population total according to a PO sampling design

## Usage

 `1` ```E.PO(y, Pik) ```

## Arguments

 `y` Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample `Pik` Vector of inclusion probabilities for each unit in the selected 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 under a PO sampling 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.PO`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# Uses the Lucy data to draw a Poisson sample data(Lucy) attach(Lucy) N <- dim(Lucy) # The population size is 2396. The expected sample size is 400 # The inclusion probability is proportional to the variable Income n <- 400 Pik<-n*Income/sum(Income) # The selected sample sam <- S.PO(N,Pik) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The inclusion probabilities of each unit in the selected smaple inclusion <- Pik[sam] # 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.PO(estima,inclusion) ```