dev.nm.stat.descriptive.covariance

Class Covariance

java.lang.Object

dev.nm.stat.descriptive.covariance.Covariance

All Implemented Interfaces:

Statistic

public class Covariance
extends Object
implements Statistic

Covariance is a measure of how much two variables change together. This implementation uses the Pearson method. That is, \[ \operatorname{Cov}(X,Y) = \mathbb{E}\!\left[(X-\mathbb{E}[X])(Y-\mathbb{E}[Y])\right] \] Note that this implementation uses N - 1 as the denominator to give an unbiased estimator of the covariance for i.i.d. observations. This implementation uses Pébay's update formula to incrementally compute the new statistic.

Paired observations

Pass equally sized arrays in matching observation order. Covariance uses the sample denominator; correlation removes the units. Both arrays must have nonzero variance for a meaningful correlation.

 import dev.nm.stat.descriptive.covariance.Covariance;
 Covariance paired = new Covariance(new double[]{1, 2, 3}, new double[]{2, 4, 6});
 assert paired.N() == 3;
 assert Math.abs(paired.value() - 2.0) < 1e-12;
 assert Math.abs(paired.correlation() - 1.0) < 1e-12;
 

See Also:

• Wikipedia: Covariance
• Wikipedia: Correlation

Constructor Summary

Constructors

Constructor and Description
Covariance() Construct an empty Covariance calculator.
Covariance(Covariance that) Copy constructor.
Covariance(double[] data1, double[] data2) Construct a Covariance calculator, initialized with two samples.

Method Summary

Modifier and Type	Method and Description
void	addData(double... data) Update the covariance statistic with more data.
void	addData(double[] data1, double[] data2) Update the covariance statistic with more data.
double	correlation() Get the correlation, i.e., Pearson's correlation coefficient.
long	N() Get the size of the sample.
String	toString()
double	value() Get the value of the statistic.

Methods inherited from class java.lang.Object

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

Constructor Detail

Covariance

public Covariance()

Construct an empty Covariance calculator.

Covariance

public Covariance(double[] data1,
                  double[] data2)

Construct a Covariance calculator, initialized with two samples. The size of the two samples must be equal.

Parameters:

data1 - the first sample

data2 - the second sample

Covariance

public Covariance(Covariance that)

Copy constructor.

Parameters:

that - a Covariance instance

Method Detail

correlation

public double correlation()

Get the correlation, i.e., Pearson's correlation coefficient.

Returns:

the correlation

addData

public void addData(double... data)

Update the covariance statistic with more data. Since this signature takes only a single array double[], we concatenate the two arrays into one.

For example, suppose we want to do

 
 addData(new double[][]{
     {1, 2, 3},
     {4, 5, 6}
 });
 
 

We can also write

 
 addData(new double[]{
     {1, 2, 3, 4, 5, 6}
 });
 
 

In the latter case, there must be an even number of data points.

Specified by:

addData in interface Statistic

Parameters:

data - a data array concatenating two samples

addData

public void addData(double[] data1,
                    double[] data2)

Update the covariance statistic with more data.

Parameters:

data1 - the first new sample

data2 - the second new sample

See Also:

"Pébay, Philippe, "Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments," Technical Report SAND2008-6212, Sandia National Laboratories, 2008."

value

public double value()

Description copied from interface: Statistic

Get the value of the statistic.

Specified by:

value in interface Statistic

Returns:

the statistic

N

public long N()

Description copied from interface: Statistic

Get the size of the sample.

Specified by:

N in interface Statistic

Returns:

the sample size

toString

public String toString()

Overrides:

toString in class Object