Package org.hipparchus.stat.correlation

Class KendallsCorrelation

java.lang.Object
org.hipparchus.stat.correlation.KendallsCorrelation
public class KendallsCorrelation extends Object
Implementation of Kendall's Tau-b rank correlation.

A pair of observations (x1, y1) and (x2, y2) are considered concordant if x1 < x2 and y1 < y2 or x2 < x1 and y2 < y1. The pair is discordant if x1 < x2 and y2 < y1 or x2 < x1 and y1 < y2. If either x1 = x2 or y1 = y2, the pair is neither concordant nor discordant.

Kendall's Tau-b is defined as: \[ \tau_b = \frac{n_c - n_d}{\sqrt{(n_0 - n_1) (n_0 - n_2)}} \]

where:

  • n0 = n * (n - 1) / 2
  • nc = Number of concordant pairs
  • nd = Number of discordant pairs
  • n1 = sum of ti * (ti - 1) / 2 for all i
  • n2 = sum of uj * (uj - 1) / 2 for all j
  • ti = Number of tied values in the ith group of ties in x
  • uj = Number of tied values in the jth group of ties in y

This implementation uses the O(n log n) algorithm described in William R. Knight's 1966 paper "A Computer Method for Calculating Kendall's Tau with Ungrouped Data" in the Journal of the American Statistical Association.

See Also:

  • Constructor Details

    • KendallsCorrelation

      public KendallsCorrelation()
      Create a KendallsCorrelation instance without data.

    • KendallsCorrelation

      public KendallsCorrelation(double[][] data)
      Create a KendallsCorrelation from a rectangular array whose columns represent values of variables to be correlated.
      Parameters:
      data - rectangular array with columns representing variables
      Throws:
      IllegalArgumentException - if the input data array is not rectangular with at least two rows and two columns.

    • KendallsCorrelation

      public KendallsCorrelation(RealMatrix matrix)
      Create a KendallsCorrelation from a RealMatrix whose columns represent variables to be correlated.
      Parameters:
      matrix - matrix with columns representing variables to correlate

  • Method Details

    • getCorrelationMatrix

      public RealMatrix getCorrelationMatrix()
      Returns the correlation matrix.
      Returns:
      correlation matrix

    • computeCorrelationMatrix

      public RealMatrix computeCorrelationMatrix(RealMatrix matrix)
      Computes the Kendall's Tau rank correlation matrix for the columns of the input matrix.
      Parameters:
      matrix - matrix with columns representing variables to correlate
      Returns:
      correlation matrix

    • computeCorrelationMatrix

      public RealMatrix computeCorrelationMatrix(double[][] matrix)
      Computes the Kendall's Tau rank correlation matrix for the columns of the input rectangular array. The columns of the array represent values of variables to be correlated.
      Parameters:
      matrix - matrix with columns representing variables to correlate
      Returns:
      correlation matrix

    • correlation

      public double correlation(double[] xArray, double[] yArray) throws MathIllegalArgumentException
      Computes the Kendall's Tau rank correlation coefficient between the two arrays.
      Parameters:
      xArray - first data array
      yArray - second data array
      Returns:
      Returns Kendall's Tau rank correlation coefficient for the two arrays
      Throws:
      MathIllegalArgumentException - if the arrays lengths do not match