com.numericalmethod.suanshu.stats.descriptive.moment

Class Kurtosis

java.lang.Object

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

All Implemented Interfaces:

Statistic, java.io.Serializable

public class Kurtosis
extends java.lang.Object
implements Statistic

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. This implementation computes the excess kurtosis. That is,

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
• "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."

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
Kurtosis() Construct an empty Kurtosis calculator.
Kurtosis(double[] data) Construct a Kurtosis calculator, initialized with a sample.
Kurtosis(Kurtosis that) Copy constructor.

Method Summary

Modifier and Type	Method and Description
void	addData(double... data) Recompute the statistic with more data, 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 - a Kurtosis calculator

Method Detail

sample

public double sample()

Get the sample kurtosis (biased estimator).

Returns:

the sample kurtosis

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()

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 java.lang.String toString()

Overrides:

toString in class java.lang.Object