# Estimation of a Population quantile Computes the estimation of a population quantile using the principles of the Horvitz-Thompson estimator ```r 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 ## See Also `HT` ## Details Returns the estimation of the population quantile of every single variable of interest ## Returns 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. ## Examples ```r ############ ## 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) ```

E.Quantile.rd function