# E.Quantile: Estimation of a Population quantile In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the estimation of a population quantile using the principles of the Horvitz-Thompson estimator

## Usage

 `1` ```E.Quantile(y, Qn, Pik) ```

## Arguments

 `y` Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample `Qn` Quantile of interest `Pik` A vector containing inclusion probabilities for each unit in the sample. If missing, the function will assign the same weights to each unit in the sample

## Details

Returns the estimation of the population quantile of every single variable of interest

## Value

The function returns a vector whose entries correspond to the estimated quantiles 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.

`HT`

## 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``` ```############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vectors y and x give the values of the variables of interest y<-c(32, 34, 46, 89, 35) x<-c(52, 60, 75, 100, 50) z<-cbind(y,x) # Inclusion probabilities for a design of size n=2 Pik<-c(0.58, 0.34, 0.48, 0.33, 0.27) # Estimation of the sample median E.Quantile(y, 0.5) # Estimation of the sample Q1 E.Quantile(x, 0.25) # Estimation of the sample Q3 E.Quantile(z, 0.75) # Estimation of the sample median E.Quantile(z, 0.5, Pik) ############ ## Example 2 ############ # Uses the Lucy data to draw a PPS sample with replacement data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income # The sample size is m=400 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) # The vector of selection probabilities of units in the sample pk.s <- res[,2] # The vector of inclusion probabilities of units in the sample Pik.s<-1-(1-pk.s)^m # The information about the sample units is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # 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) # Estimation of sample median E.Quantile(estima,0.5,Pik.s) ```

### Example output

``` 35
 52
 39.4 66.0
 35 60
The following objects are masked from Lucy:

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

The following objects are masked from data (pos = 3):

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

The following objects are masked from Lucy:

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

 "ID"        "Ubication" "Level"     "Zone"      "Income"    "Employees"
 "Taxes"     "SPAM"
 328.0  69.0  10.5
```

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