Package com.imsl.stat

Class EmpiricalQuantiles

java.lang.Object
com.imsl.stat.EmpiricalQuantiles
All Implemented Interfaces:
Serializable, Cloneable
public class EmpiricalQuantiles extends Object implements Serializable, Cloneable
Computes empirical quantiles.

The class EmpiricalQuantiles determines the empirical quantiles, as indicated in the array qProp, from the data in x. The algorithm first checks to see if x is sorted; if x is not sorted, the algorithm does either a complete or partial sort, depending on how many order statistics are required to compute the quantiles requested. The algorithm returns the empirical quantiles and, for each quantile, the two order statistics from the sample that are at least as large and at least as small as the quantile. For a sample of size n, the quantile corresponding to the proportion p is defined as $$Q(p) = (1 - f)x_{(j)} + fx_{(j+1)} $$ where \(j = \lfloor p(n+1) \rfloor \), \(f = p(n+1) - j\), and \(x_{(j)}\), is the j-th order statistic, if \(1 \leq j \le n\); otherwise, the empirical quantile is the smallest or largest order statistic.

See Also:

  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    static class 
    EmpiricalQuantiles.ScaleFactorZeroException
    The computations cannot continue because a scale factor is zero.

  • Constructor Summary

    Constructors
    Constructor
    Description
    EmpiricalQuantiles(double[] x, double[] qProp)
    Constructor for EmpiricalQuantiles.

  • Method Summary

    Modifier and Type
    Method
    Description
    final double[]
    getQ()
    Returns the empirical quantiles.
    int
    getTotalMissing()
    Returns the total number of missing values.
    final double[]
    getXHi()
    Returns the smallest element of x greater than or equal to the desired quantile.
    final double[]
    getXLo()
    Returns the largest element of x less than or equal to the desired quantile.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • EmpiricalQuantiles

      public EmpiricalQuantiles(double[] x, double[] qProp)
      Constructor for EmpiricalQuantiles.
      Parameters:
      x - A double array containing the data.
      qProp - A double array containing the quantile proportions.

  • Method Details

    • getTotalMissing

      public int getTotalMissing()
      Returns the total number of missing values.
      Returns:
      an int scalar value representing the total number of missing values (NaN) in input x.

    • getQ

      public final double[] getQ()
      Returns the empirical quantiles.
      Returns:
      A double array containing the empirical quantiles. Q[i] corresponds to the empirical quantile at proportion qProp[i]. The quantiles are determined by linear interpolation between adjacent ordered sample values.

    • getXLo

      public final double[] getXLo()
      Returns the largest element of x less than or equal to the desired quantile.
      Returns:
      A double array containing the largest element of x less than or equal to the desired quantile.

    • getXHi

      public final double[] getXHi()
      Returns the smallest element of x greater than or equal to the desired quantile.
      Returns:
      A double array containing the smallest element of x greater than or equal to the desired quantile.