KendallsCorrelation
org.apache.commons.math3.stat.correlation

Class KendallsCorrelation



  • public class KendallsCorrelationextends 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:

     taub = (nc - nd) / sqrt((n0 - n1) * (n0 - n2)) 

    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:
    Kendall tau rank correlation coefficient (Wikipedia), A Computer Method for Calculating Kendall's Tau with Ungrouped Data
    • Constructor Detail

      • 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 Detail

      • 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 DimensionMismatchException
        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:
        DimensionMismatchException - if the arrays lengths do not match

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