com.numericalmethod.suanshu.stats.descriptive.moment
Class Variance

java.lang.Object
  com.numericalmethod.suanshu.stats.descriptive.moment.Variance

All Implemented Interfaces:

Statistic

public class Variance
extends java.lang.Object
implements Statistic

The variance of a sample is the average squared deviations from the sample mean. It measures the amount of variation the sample values have.

 Var(X, Y) = E[(X - E(X))2]
 

This implementation uses Chan's update formula to incrementally compute the new statistic.

The R equivalent function is sd.

See Also:

• Wikipedia: Variance
• Wikipedia: Algorithms for calculating variance
• "Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1979), "Updating Formulae and a Pairwise Algorithm for Computing Sample Variances," Technical Report STAN-CS-79-773, Department of Computer Science, Stanford University."

Field Summary

boolean

unbiased indicate whether the variance calculation is unbiased or not; true iff unbiased

Constructor Summary

Variance()
Construct an empty Variance calculator.

Variance(double[] data)
Construct an unbiased Variance calculator.

Variance(double[] data, boolean unbiased)
Construct a Variance calculator, initialized with a sample.

Variance(Variance that)
Copy constructor.

Method Summary

void	addData(double... data) Recompute the statistic, incrementally if possible.
long	N() Get the size of the sample.
double	standardDeviation() Get the standard deviation of the sample, which is the square root of the variance.
java.lang.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

Field Detail

unbiased

public final boolean unbiased

indicate whether the variance calculation is unbiased or not; true iff unbiased

Constructor Detail

Variance

public Variance()

Construct an empty Variance calculator.

Variance

public Variance(double[] data,
                boolean unbiased)

Construct a Variance calculator, initialized with a sample.

Parameters:

data - a sample

unbiased - true if the variance calculation uses the unbiased formula

Variance

public Variance(double[] data)

Construct an unbiased Variance calculator.

Parameters:

data - a sample

Variance

public Variance(Variance that)

Copy constructor.

Parameters:

that - another Variance object

Method Detail

addData

public void addData(double... data)

Description copied from interface: Statistic

Recompute the statistic, incrementally if possible.

Specified by:

addData in interface Statistic

Parameters:

data - an array of new items

value

public double value()

Description copied from interface: Statistic

Get the value of the statistic.

Specified by:

value in interface Statistic

Returns:

the statistic

standardDeviation

public double standardDeviation()

Get the standard deviation of the sample, which is the square root of the variance.

Returns:

the standard deviation

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 java.lang.String toString()

Overrides:

toString in class java.lang.Object