dev.nm.stat.descriptive.moment

Class Variance

java.lang.Object

dev.nm.stat.descriptive.moment.Variance

All Implemented Interfaces:

Statistic

public class Variance
extends 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. That is, \[ \operatorname{Var}(X) = \mathbb{E}\!\left[(X-\mathbb{E}[X])^2\right] \] This implementation uses Chan's update formula to incrementally compute the new statistic.

The R equivalent function is var.

Choosing the denominator

The no-argument and one-array constructors use the unbiased sample variance with denominator N - 1. Pass false as the second constructor argument to use denominator N. The current implementation returns zero for fewer than two observations in either mode; callers must check N() before interpreting that value as an estimate.

Updates append observations; empty batches leave all accumulated values unchanged. standardDeviation() uses the same denominator choice.

Independent sample snapshots

The copy constructor preserves the denominator choice and creates an independently updatable calculator.

 import dev.nm.stat.descriptive.moment.Variance;
 Variance original = new Variance(new double[]{1, 2, 3, 4});
 Variance snapshot = new Variance(original);
 snapshot.addData();
 snapshot.addData(5);
 assert original.N() == 4;
 assert Math.abs(original.value() - 5.0 / 3.0) < 1e-12;
 assert snapshot.N() == 5;
 assert Math.abs(snapshot.value() - 2.5) < 1e-12;
 

See Also:

Mean,

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

Constructor Summary

Constructors

Constructor and Description
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

Modifier and Type	Method and Description
void	addData(double... data) Recompute the statistic with more data, incrementally if possible.
double	mean() Get the sample mean.
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.
String	toString()
double	value() Returns the accumulated variance using the configured denominator.

Methods inherited from class java.lang.Object

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

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 - a Variance calculator

Method Detail

standardDeviation

public double standardDeviation()

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

Returns:

the standard deviation

addData

public void addData(double... data)

Description copied from interface: Statistic

Recompute the statistic with more data, incrementally if possible.

Specified by:

addData in interface Statistic

Parameters:

data - an array of new items

value

public double value()

Returns the accumulated variance using the configured denominator.

Specified by:

value in interface Statistic

Returns:

variance, or zero when fewer than two observations have been added

See Also:

N()

mean

public double mean()

Get the sample mean.

Returns:

the mean

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