dev.nm.stat.descriptive.moment

Class Skewness

java.lang.Object

dev.nm.stat.descriptive.moment.Skewness

All Implemented Interfaces:

Statistic

public class Skewness
extends Object
implements Statistic

Skewness is a measure of the asymmetry of the probability distribution. A distribution may either be positively or negatively skewed. For positive skew (or right-skewed), the right tail is longer. The mass of the distribution is concentrated on the left. For negative skew (or left-skewed), the left tail is longer. The mass of the distribution is concentrated on the right. The definition is: \[ \gamma_1 = \mathbb{E}\!\left[\left(\frac{X-\mathbb{E}[X]}{\sigma}\right)^3\right] \] This implementation uses Chan's update formula to incrementally compute the new statistic.

The R equivalent function is skewness.

See Also:

• Wikipedia: Skewness
• 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

Constructors

Constructor and Description
Skewness() Construct an empty Skewness calculator.
Skewness(double[] data) Construct a Skewness calculator, initialized with a sample.
Skewness(Skewness 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	sample() Get the sample skewness (biased estimator).
String	toString()
double	value() Get the value of the statistic.
double	variance() Get the (unbiased) variance.

Methods inherited from class java.lang.Object

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

Constructor Detail

Skewness

public Skewness()

Construct an empty Skewness calculator.

Skewness

public Skewness(double[] data)

Construct a Skewness calculator, initialized with a sample.

Parameters:

data - a sample

Skewness

public Skewness(Skewness that)

Copy constructor.

Parameters:

that - a Skewness calculator

Method Detail

sample

public double sample()

Get the sample skewness (biased estimator).

Returns:

the sample skewness

mean

public double mean()

Get the sample mean.

Returns:

the mean

variance

public double variance()

Get the (unbiased) variance.

Returns:

the (unbiased) variance

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 String toString()

Overrides:

toString in class Object