de.lmu.ifi.dbs.elki.math

Class StatisticalMoments

java.lang.Object

de.lmu.ifi.dbs.elki.math.Mean

de.lmu.ifi.dbs.elki.math.MeanVariance

de.lmu.ifi.dbs.elki.math.MeanVarianceMinMax

de.lmu.ifi.dbs.elki.math.StatisticalMoments

@Reference(authors="Erich Schubert, Michael Gertz",title="Numerically Stable Parallel Computation of (Co-)Variance",booktitle="Proc. 30th Int. Conf. Scientific and Statistical Database Management (SSDBM 2018)",url="https://doi.org/10.1145/3221269.3223036",bibkey="DBLP:conf/ssdbm/SchubertG18") @Reference(authors="T. B. Terriberry",title="Computing Higher-Order Moments Online",booktitle="",url="http://people.xiph.org/~tterribe/notes/homs.html",bibkey="web/Terriberry07") @Reference(authors="P. P\u00e9bay",title="Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments",booktitle="Sandia Report SAND2008-6212, Sandia National Laboratories",url="https://prod.sandia.gov/techlib-noauth/access-control.cgi/2008/086212.pdf",bibkey="tr/sandia/Pebay08") @Reference(authors="E. A. Youngs, E. M. Cramer",title="Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms",booktitle="Technometrics 13(3)",url="https://doi.org/10.1080/00401706.1971.10488826",bibkey="doi:10.1080/00401706.1971.10488826")
public class StatisticalMoments
extends MeanVarianceMinMax

Track various statistical moments, including mean, variance, skewness and kurtosis.

References:

An exhaustive performance study:

Erich Schubert, Michael Gertz
Numerically Stable Parallel Computation of (Co-)Variance
Proc. 30th Int. Conf. Scientific and Statistical Database Management (SSDBM 2018)

Details on higher order moments:

T. B. Terriberry
Computing Higher-Order Moments Online
http://people.xiph.org/~tterribe/notes/homs.html

General recurrence, for higher order moments, can be found in:

P. Pébay
Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments
Sandia Report SAND2008-6212, Sandia National Laboratories

But our approach also uses parts of

E. A. Youngs and E. M. Cramer
Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms
Technometrics 13(3), 1971

Since:

0.6.0

Author:

Erich Schubert

Field Summary

Fields

Modifier and Type	Field and Description
(package private) double	m3 Third moment.
(package private) double	m4 Fourth moment.

Fields inherited from class de.lmu.ifi.dbs.elki.math.MeanVarianceMinMax

max, min

Fields inherited from class de.lmu.ifi.dbs.elki.math.MeanVariance

m2

Fields inherited from class de.lmu.ifi.dbs.elki.math.Mean

n, sum

Constructor Summary

Constructors

Constructor and Description
StatisticalMoments() Empty constructor
StatisticalMoments(StatisticalMoments other) Constructor from other instance

Method Summary

Modifier and Type	Method and Description
double	getNaiveExcessKurtosis() Get the kurtosis using naive variance.
double	getNaiveKurtosis() Get the kurtosis using naive variance.
double	getNaiveSkewness() Get the skewness using naive variance.
double	getSampleExcessKurtosis() Get the kurtosis using sample variance.
double	getSampleKurtosis() Get the kurtosis using sample variance.
double	getSampleSkewness() Get the skewness using sample variance.
static StatisticalMoments[]	newArray(int dimensionality) Create and initialize a new array of MeanVariance
void	put(double val) Add a single value with weight 1.0
StatisticalMoments	put(double[] vals) Add values with weight 1.0
StatisticalMoments	put(double[] vals, double[] weights) Add values with weight 1.0
void	put(double val, double weight) Add data with a given weight.
void	put(Mean other) Join the data of another MeanVariance instance.
void	reset() Reset the value.
java.lang.String	toString()

Methods inherited from class de.lmu.ifi.dbs.elki.math.MeanVarianceMinMax

getDiff, getDoubleMinMax, getMax, getMin

Methods inherited from class de.lmu.ifi.dbs.elki.math.MeanVariance

getNaiveStddev, getNaiveVariance, getSampleStddev, getSampleVariance, getSumOfSquares

Methods inherited from class de.lmu.ifi.dbs.elki.math.Mean

getCount, getMean, highPrecision, of

Methods inherited from class java.lang.Object

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

Field Detail

m3

double m3

Third moment.

m4

double m4

Fourth moment.

Constructor Detail

StatisticalMoments

public StatisticalMoments()

Empty constructor

StatisticalMoments

public StatisticalMoments(StatisticalMoments other)

Constructor from other instance

Parameters:

other - other instance to copy data from.

Method Detail

put

public void put(double val)

Add a single value with weight 1.0

Overrides:

put in class MeanVarianceMinMax

Parameters:

val - Value

put

public void put(double val,
                double weight)

Add data with a given weight.

Overrides:

put in class MeanVarianceMinMax

Parameters:

val - data

weight - weight

put

public void put(Mean other)

Join the data of another MeanVariance instance.

Overrides:

put in class MeanVarianceMinMax

Parameters:

other - Data to join with

put

public StatisticalMoments put(double[] vals)

Description copied from class: MeanVarianceMinMax

Add values with weight 1.0

Overrides:

put in class MeanVarianceMinMax

Parameters:

vals - Values

Returns:

this

put

public StatisticalMoments put(double[] vals,
                              double[] weights)

Description copied from class: Mean

Add values with weight 1.0

Overrides:

put in class MeanVarianceMinMax

Parameters:

vals - Values

Returns:

this

getSampleSkewness

public double getSampleSkewness()

Get the skewness using sample variance.

Returns:

Skewness

getNaiveSkewness

public double getNaiveSkewness()

Get the skewness using naive variance.

Returns:

Skewness

getSampleKurtosis

public double getSampleKurtosis()

Get the kurtosis using sample variance. Note: this formula does not include the correction factor, such that a normal distribution should be 0.

Returns:

Kurtosis

getNaiveKurtosis

public double getNaiveKurtosis()

Get the kurtosis using naive variance. Note: this formula does not include the -3 term.

Returns:

Kurtosis

getSampleExcessKurtosis

public double getSampleExcessKurtosis()

Get the kurtosis using sample variance. Note: this formula does include the correction factor, such that a normal distribution should be 0.

Returns:

Kurtosis

getNaiveExcessKurtosis

public double getNaiveExcessKurtosis()

Get the kurtosis using naive variance. Note: this formula does include the -3 term.

Returns:

Kurtosis

newArray

public static StatisticalMoments[] newArray(int dimensionality)

Create and initialize a new array of MeanVariance

Parameters:

dimensionality - Dimensionality

Returns:

New and initialized Array

toString

public java.lang.String toString()

Overrides:

toString in class MeanVarianceMinMax

reset

public void reset()

Description copied from class: Mean

Reset the value.

Overrides:

reset in class MeanVarianceMinMax