org.apache.commons.math3.stat.correlation

Class KendallsCorrelation

java.lang.Object

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

public class KendallsCorrelation
extends java.lang.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
• n_c = Number of concordant pairs
• n_d = Number of discordant pairs
• n₁ = sum of t_i * (t_i - 1) / 2 for all i
• n₂ = sum of u_j * (u_j - 1) / 2 for all j
• t_i = Number of tied values in the i^th group of ties in x
• u_j = Number of tied values in the j^th 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.

Since:

3.3

See Also:

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

Field Summary

Fields

Modifier and Type	Field and Description
private RealMatrix	correlationMatrix correlation matrix

Constructor Summary

Constructors

Constructor and Description
KendallsCorrelation() Create a KendallsCorrelation instance without data.
KendallsCorrelation(double[][] data) Create a KendallsCorrelation from a rectangular array whose columns represent values of variables to be correlated.
KendallsCorrelation(RealMatrix matrix) Create a KendallsCorrelation from a RealMatrix whose columns represent variables to be correlated.

Method Summary

Methods

Modifier and Type	Method and Description
RealMatrix	computeCorrelationMatrix(double[][] matrix) Computes the Kendall's Tau rank correlation matrix for the columns of the input rectangular array.
RealMatrix	computeCorrelationMatrix(RealMatrix matrix) Computes the Kendall's Tau rank correlation matrix for the columns of the input matrix.
double	correlation(double[] xArray, double[] yArray) Computes the Kendall's Tau rank correlation coefficient between the two arrays.
RealMatrix	getCorrelationMatrix() Returns the correlation matrix.
private static long	sum(long n) Returns the sum of the number from 1 ..

Methods inherited from class java.lang.Object

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

Field Detail

correlationMatrix

private final RealMatrix correlationMatrix

correlation matrix

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:

java.lang.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

sum

private static long sum(long n)

Returns the sum of the number from 1 .. n according to Gauss' summation formula: \[ \sum\limits_{k=1}^n k = \frac{n(n + 1)}{2} \]

Parameters:

n - the summation end

Returns:

the sum of the number from 1 to n