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

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

All Implemented Interfaces:

Statistic

public class Moments
extends java.lang.Object
implements Statistic

Compute the central moment of a data set incrementally. The n-th moment is the expected value of the n-th power of the differences from the mean.

 μk = E[(X - E(X))k]
 

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

See Also:

• Pébay, Philippe (2008). Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments. Technical Report SAND2008-6212. Sandia National Laboratories.
• Wikipedia: Moment (mathematics)

Field Summary

int	order the highest moment to compute

Constructor Summary

Moments(int order)
Construct an instance to compute all moments up to the order-th moment.

Moments(int order, double... data)
Construct an instance to compute all moments up to the order-th moment, initialized with a sample.

Moments(Moments that)
Copy constructor.

Method Summary

void	addData(double... data) Recompute the statistic, incrementally if possible.
double	centralMoment(int k) Get the value of the k-th central moment.
long	N() Get the size of the sample.
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

order

public final int order

the highest moment to compute

Constructor Detail

Moments

public Moments(int order)

Construct an instance to compute all moments up to the order-th moment.

Parameters:

order - the number of the highest moment

Moments

public Moments(int order,
               double... data)

Construct an instance to compute all moments up to the order-th moment, initialized with a sample.

Parameters:

order - the number of the highest moment

data - a sample

Moments

public Moments(Moments that)

Copy constructor.

Parameters:

that - another Moments 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

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

centralMoment

public double centralMoment(int k)

Get the value of the k-th central moment. This method can be used to compute the lower moments.

For example, centralMoment(1) is the mean. For higher central moments, they do not correspond to variance, skew, kurtosis, etc.

Parameters:

k - the order of the moment

Returns:

the value of the k-th central moment

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object