Estimation of a Population quantile
Computes the estimation of a population quantile using the principles of the Horvitz-Thompson estimator
E.Quantile(y, Qn, Pik)
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 |
Returns the estimation of the population quantile of every single variable of interest
The function returns a vector whose entries correspond to the estimated quantiles of the variables of interest
Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com
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.
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## Example 1
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# 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)
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## Example 2
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# 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.