E.Quantile {TeachingSampling}

Estimation of a Population quantile

Description

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

Usage

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 [e-mail]

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.

See Also

HT

Examples

############
## 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)