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

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

All Implemented Interfaces:

Statistic

public class Kurtosis
extends java.lang.Object
implements Statistic

This defines the excess kurtosis.

Kurtosis measures the "peakedness" of the probability distribution of a real-valued random variable. Higher kurtosis means that there are more infrequent extreme deviations than frequent modestly sized deviations, hence a fatter tail.

 γ = E[((X - E(X)) / σ)4]
 

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

The R equivalent function is kurtosis.

See Also:

• Wikipedia: Kurtosis
• 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."

Constructor Summary

Kurtosis()
Construct an empty Kurtosis calculator.

Kurtosis(double[] data)
Construct a Kurtosis calculator, initialized with a sample.

Kurtosis(Kurtosis that)
Copy constructor.

Method Summary

void	addData(double... data) Recompute the statistic, incrementally if possible.
long	N() Get the size of the sample.
double	sample() Get the sample kurtosis (biased estimator).
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

Constructor Detail

Kurtosis

public Kurtosis()

Construct an empty Kurtosis calculator.

Kurtosis

public Kurtosis(double[] data)

Construct a Kurtosis calculator, initialized with a sample.

Parameters:

data - a sample

Kurtosis

public Kurtosis(Kurtosis that)

Copy constructor.

Parameters:

that - another Kurtosis 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

sample

public double sample()

Get the sample kurtosis (biased estimator).

Returns:

the sample kurtosis

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