Example: Empirical Quantiles
In this example, five empirical quantiles from a sample of size 30 are obtained. Notice that the 0.5 quantile corresponds to the sample median. The data are from Hinkley (1977) and Velleman and Hoaglin (1981). They are the measurements (in inches) of precipitation in Minneapolis/St. Paul during the month of March for 30 consecutive years.
using System;
using Imsl.Stat;
public class EmpiricalQuantilesEx1
{
public static void Main(String[] args)
{
double[] x = {0.77, 1.74, 0.81, 1.20, 1.95, 1.20, 0.47, 1.43, 3.37,
2.20, 3.00, 3.09, 1.51, 2.10, 0.52, 1.62, 1.31, 0.32, 0.59,
0.81, 2.81, 1.87, 1.18, 1.35, 4.75, 2.48, 0.96, 1.89, 0.90,
2.05};
double[] qProp = {0.01, 0.5, 0.90, 0.95, 0.99};
EmpiricalQuantiles eq = new EmpiricalQuantiles(x, qProp);
double[] Q = eq.GetQ();
double[] XLo = eq.GetXLo();
double[] XHi = eq.GetXHi();
Console.WriteLine(" Smaller Empirical Larger");
Console.WriteLine(" Quantile Datum Quantile Datum");
for (int i=0; i < qProp.Length; i++)
Console.WriteLine(" {0}\t\t{1}\t\t{2}\t\t{3}",
qProp[i], XLo[i], Q[i], XHi[i]);
}
}
Output
Smaller Empirical Larger
Quantile Datum Quantile Datum
0.01 0.32 0.32 0.32
0.5 1.43 1.47 1.51
0.9 3 3.081 3.09
0.95 3.37 3.991 4.75
0.99 4.75 4.75 4.75
Link to C# source.