fr.cnes.sirius.patrius.math.stat.descriptive.moment

Class Variance

java.lang.Object

fr.cnes.sirius.patrius.math.stat.descriptive.AbstractUnivariateStatistic

fr.cnes.sirius.patrius.math.stat.descriptive.AbstractStorelessUnivariateStatistic

fr.cnes.sirius.patrius.math.stat.descriptive.moment.Variance

All Implemented Interfaces:

StorelessUnivariateStatistic, UnivariateStatistic, WeightedEvaluation, MathArrays.Function, Serializable

public class Variance
extends AbstractStorelessUnivariateStatistic
implements Serializable, WeightedEvaluation

Computes the variance of the available values. By default, the unbiased "sample variance" definitional formula is used:

variance = sum((x_i - mean)^2) / (n - 1)

where mean is the Mean and n is the number of sample observations.

The definitional formula does not have good numerical properties, so this implementation does not compute the statistic using the definitional formula.

• The getResult method computes the variance using updating formulas based on West's algorithm, as described in Chan, T. F. and J. G. Lewis 1979, Communications of the ACM, vol. 22 no. 9, pp. 526-531.
• The evaluate methods leverage the fact that they have the full array of values in memory to execute a two-pass algorithm. Specifically, these methods use the "corrected two-pass algorithm" from Chan, Golub, Levesque, Algorithms for Computing the Sample Variance, American Statistician, vol. 37, no. 3 (1983) pp. 242-247.

Note that adding values using increment or incrementAll and then executing getResult will sometimes give a different, less accurate, result than executing evaluate with the full array of values. The former approach should only be used when the full array of values is not available.

The "population variance" ( sum((x_i - mean)^2) / n ) can also be computed using this statistic. The isBiasCorrected property determines whether the "population" or "sample" value is returned by the evaluate and getResult methods. To compute population variances, set this property to false.

Note that this implementation is not synchronized. If multiple threads access an instance of this class concurrently, and at least one of the threads invokes the increment() or clear() method, it must be synchronized externally.

Version:

$Id: Variance.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected boolean	incMoment Whether or not increment(double) should increment the internal second moment.
protected SecondMoment	moment SecondMoment is used in incremental calculation of Variance

Constructor Summary

Constructors

Constructor and Description
Variance() Constructs a Variance with default (true) isBiasCorrected property.
Variance(boolean isBiasCorrectedIn) Constructs a Variance with the specified isBiasCorrected property
Variance(boolean isBiasCorrectedIn, SecondMoment m2) Constructs a Variance with the specified isBiasCorrected property and the supplied external second moment.
Variance(SecondMoment m2) Constructs a Variance based on an external second moment.
Variance(Variance original) Copy constructor, creates a new Variance identical to the original

Method Summary

Methods

Modifier and Type	Method and Description
void	clear() Clears the internal state of the Statistic
Variance	copy() Returns a copy of the statistic with the same internal state.
static void	copy(Variance source, Variance dest) Copies source to dest.
double	evaluate(double[] values) Returns the variance of the entries in the input array, or Double.NaN if the array is empty.
double	evaluate(double[] values, double mean) Returns the variance of the entries in the input array, using the precomputed mean value.
double	evaluate(double[] values, double[] weights) Returns the weighted variance of the entries in the the input array.
double	evaluate(double[] values, double[] weights, double mean) Returns the weighted variance of the values in the input array, using the precomputed weighted mean value.
double	evaluate(double[] values, double[] weights, double mean, int begin, int length) Returns the weighted variance of the entries in the specified portion of the input array, using the precomputed weighted mean value.
double	evaluate(double[] values, double[] weights, int begin, int length) Returns the weighted variance of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
double	evaluate(double[] values, double mean, int begin, int length) Returns the variance of the entries in the specified portion of the input array, using the precomputed mean value.
double	evaluate(double[] values, int begin, int length) Returns the variance of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
long	getN() Returns the number of values that have been added.
double	getResult() Returns the current value of the Statistic.
void	increment(double d) Updates the internal state of the statistic to reflect the addition of the new value.
boolean	isBiasCorrected()
void	setBiasCorrected(boolean biasCorrected)

Methods inherited from class fr.cnes.sirius.patrius.math.stat.descriptive.AbstractStorelessUnivariateStatistic

equals, hashCode, incrementAll, incrementAll

Methods inherited from class fr.cnes.sirius.patrius.math.stat.descriptive.AbstractUnivariateStatistic

evaluate, getData, getDataRef, setData, setData, test, test, test, test

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Field Detail

moment

protected SecondMoment moment

SecondMoment is used in incremental calculation of Variance

incMoment

protected boolean incMoment

Whether or not increment(double) should increment the internal second moment. When a Variance is constructed with an external SecondMoment as a constructor parameter, this property is set to false and increments must be applied to the second moment directly.

Constructor Detail

Variance

public Variance()

Constructs a Variance with default (true) isBiasCorrected property.

Variance

public Variance(SecondMoment m2)

Constructs a Variance based on an external second moment. When this constructor is used, the statistic may only be incremented via the moment, i.e., increment(double) does nothing; whereas m2.increment(value) increments both m2 and the Variance instance constructed from it.

Parameters:

m2 - the SecondMoment (Third or Fourth moments work here as well.)

Variance

public Variance(boolean isBiasCorrectedIn)

Constructs a Variance with the specified isBiasCorrected property

Parameters:

isBiasCorrectedIn - setting for bias correction - true means bias will be corrected and is equivalent to using the argumentless constructor

Variance

public Variance(boolean isBiasCorrectedIn,
        SecondMoment m2)

Constructs a Variance with the specified isBiasCorrected property and the supplied external second moment.

Parameters:

isBiasCorrectedIn - setting for bias correction - true means bias will be corrected

m2 - the SecondMoment (Third or Fourth moments work here as well.)

Variance

public Variance(Variance original)

Copy constructor, creates a new Variance identical to the original

Parameters:

original - the Variance instance to copy

Throws:

NullArgumentException - if original is null

Method Detail

increment

public void increment(double d)

Updates the internal state of the statistic to reflect the addition of the new value.

If all values are available, it is more accurate to use evaluate(double[]) rather than adding values one at a time using this method and then executing getResult(), since evaluate leverages the fact that is has the full list of values together to execute a two-pass algorithm. See Variance.

Note also that when Variance(SecondMoment) is used to create a Variance, this method does nothing. In that case, the SecondMoment should be incremented directly.

Specified by:

increment in interface StorelessUnivariateStatistic

Specified by:

increment in class AbstractStorelessUnivariateStatistic

Parameters:

d - the new value.

getResult

public double getResult()

Returns the current value of the Statistic.

Specified by:

getResult in interface StorelessUnivariateStatistic

Specified by:

getResult in class AbstractStorelessUnivariateStatistic

Returns:

value of the statistic, Double.NaN if it has been cleared or just instantiated.

getN

public long getN()

Returns the number of values that have been added.

Specified by:

getN in interface StorelessUnivariateStatistic

Returns:

the number of values.

clear

public void clear()

Clears the internal state of the Statistic

Specified by:

clear in interface StorelessUnivariateStatistic

Specified by:

clear in class AbstractStorelessUnivariateStatistic

evaluate

public double evaluate(double[] values)

Returns the variance of the entries in the input array, or Double.NaN if the array is empty.

See Variance for details on the computing algorithm.

Returns 0 for a single-value (i.e. length = 1) sample.

Throws MathIllegalArgumentException if the array is null.

Does not change the internal state of the statistic.

Specified by:

evaluate in interface UnivariateStatistic

Specified by:

evaluate in interface MathArrays.Function

Overrides:

evaluate in class AbstractStorelessUnivariateStatistic

Parameters:

values - the input array

Returns:

the variance of the values or Double.NaN if length = 0

Throws:

MathIllegalArgumentException - if the array is null

See Also:

UnivariateStatistic.evaluate(double[])

evaluate

public double evaluate(double[] values,
              int begin,
              int length)

Returns the variance of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.

See Variance for details on the computing algorithm.

Returns 0 for a single-value (i.e. length = 1) sample.

Does not change the internal state of the statistic.

Throws MathIllegalArgumentException if the array is null.

Specified by:

evaluate in interface UnivariateStatistic

Specified by:

evaluate in interface MathArrays.Function

Overrides:

evaluate in class AbstractStorelessUnivariateStatistic

Parameters:

values - the input array

begin - index of the first array element to include

length - the number of elements to include

Returns:

the variance of the values or Double.NaN if length = 0

Throws:

MathIllegalArgumentException - if the array is null or the array index parameters are not valid

See Also:

UnivariateStatistic.evaluate(double[], int, int)

evaluate

public double evaluate(double[] values,
              double[] weights,
              int begin,
              int length)

Returns the weighted variance of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.

Uses the formula

   Σ(weights[i]*(values[i] - weightedMean)2)/(Σ(weights[i]) - 1)
 

where weightedMean is the weighted mean

This formula will not return the same result as the unweighted variance when all weights are equal, unless all weights are equal to 1. The formula assumes that weights are to be treated as "expansion values," as will be the case if for example the weights represent frequency counts. To normalize weights so that the denominator in the variance computation equals the length of the input vector minus one, use

   evaluate(values, MathArrays.normalizeArray(weights, values.length)); 
 

Returns 0 for a single-value (i.e. length = 1) sample.

Throws IllegalArgumentException if any of the following are true:

• the values array is null
• the weights array is null
• the weights array does not have the same length as the values array
• the weights array contains one or more infinite values
• the weights array contains one or more NaN values
• the weights array contains negative values
• the start and length arguments do not determine a valid array

Does not change the internal state of the statistic.

Throws MathIllegalArgumentException if either array is null.

Specified by:

evaluate in interface WeightedEvaluation

Parameters:

values - the input array

weights - the weights array

begin - index of the first array element to include

length - the number of elements to include

Returns:

the weighted variance of the values or Double.NaN if length = 0

Throws:

MathIllegalArgumentException - if the parameters are not valid

Since:

2.1

evaluate

public double evaluate(double[] values,
              double[] weights)

Returns the weighted variance of the entries in the the input array.

Uses the formula

   Σ(weights[i]*(values[i] - weightedMean)2)/(Σ(weights[i]) - 1)
 

where weightedMean is the weighted mean

This formula will not return the same result as the unweighted variance when all weights are equal, unless all weights are equal to 1. The formula assumes that weights are to be treated as "expansion values," as will be the case if for example the weights represent frequency counts. To normalize weights so that the denominator in the variance computation equals the length of the input vector minus one, use

   evaluate(values, MathArrays.normalizeArray(weights, values.length)); 
 

Returns 0 for a single-value (i.e. length = 1) sample.

Throws MathIllegalArgumentException if any of the following are true:

• the values array is null
• the weights array is null
• the weights array does not have the same length as the values array
• the weights array contains one or more infinite values
• the weights array contains one or more NaN values
• the weights array contains negative values

Does not change the internal state of the statistic.

Throws MathIllegalArgumentException if either array is null.

Specified by:

evaluate in interface WeightedEvaluation

Parameters:

values - the input array

weights - the weights array

Returns:

the weighted variance of the values

Throws:

MathIllegalArgumentException - if the parameters are not valid

Since:

2.1

evaluate

public double evaluate(double[] values,
              double mean,
              int begin,
              int length)

Returns the variance of the entries in the specified portion of the input array, using the precomputed mean value. Returns Double.NaN if the designated subarray is empty.

See Variance for details on the computing algorithm.

The formula used assumes that the supplied mean value is the arithmetic mean of the sample data, not a known population parameter. This method is supplied only to save computation when the mean has already been computed.

Returns 0 for a single-value (i.e. length = 1) sample.

Throws MathIllegalArgumentException if the array is null.

Does not change the internal state of the statistic.

Parameters:

values - the input array

mean - the precomputed mean value

begin - index of the first array element to include

length - the number of elements to include

Returns:

the variance of the values or Double.NaN if length = 0

Throws:

MathIllegalArgumentException - if the array is null or the array index parameters are not valid

evaluate

public double evaluate(double[] values,
              double mean)

Returns the variance of the entries in the input array, using the precomputed mean value. Returns Double.NaN if the array is empty.

See Variance for details on the computing algorithm.

If isBiasCorrected is true the formula used assumes that the supplied mean value is the arithmetic mean of the sample data, not a known population parameter. If the mean is a known population parameter, or if the "population" version of the variance is desired, set isBiasCorrected to false before invoking this method.

Returns 0 for a single-value (i.e. length = 1) sample.

Throws MathIllegalArgumentException if the array is null.

Does not change the internal state of the statistic.

Parameters:

values - the input array

mean - the precomputed mean value

Returns:

the variance of the values or Double.NaN if the array is empty

Throws:

MathIllegalArgumentException - if the array is null

evaluate

public double evaluate(double[] values,
              double[] weights,
              double mean,
              int begin,
              int length)

Returns the weighted variance of the entries in the specified portion of the input array, using the precomputed weighted mean value. Returns Double.NaN if the designated subarray is empty.

Uses the formula

   Σ(weights[i]*(values[i] - mean)2)/(Σ(weights[i]) - 1)
 

The formula used assumes that the supplied mean value is the weighted arithmetic mean of the sample data, not a known population parameter. This method is supplied only to save computation when the mean has already been computed.

This formula will not return the same result as the unweighted variance when all weights are equal, unless all weights are equal to 1. The formula assumes that weights are to be treated as "expansion values," as will be the case if for example the weights represent frequency counts. To normalize weights so that the denominator in the variance computation equals the length of the input vector minus one, use

   evaluate(values, MathArrays.normalizeArray(weights, values.length), mean); 
 

Returns 0 for a single-value (i.e. length = 1) sample.

Throws MathIllegalArgumentException if any of the following are true:

• the values array is null
• the weights array is null
• the weights array does not have the same length as the values array
• the weights array contains one or more infinite values
• the weights array contains one or more NaN values
• the weights array contains negative values
• the start and length arguments do not determine a valid array

Does not change the internal state of the statistic.

Parameters:

values - the input array

weights - the weights array

mean - the precomputed weighted mean value

begin - index of the first array element to include

length - the number of elements to include

Returns:

the variance of the values or Double.NaN if length = 0

Throws:

MathIllegalArgumentException - if the parameters are not valid

Since:

2.1

evaluate

public double evaluate(double[] values,
              double[] weights,
              double mean)

Returns the weighted variance of the values in the input array, using the precomputed weighted mean value.

Uses the formula

   Σ(weights[i]*(values[i] - mean)2)/(Σ(weights[i]) - 1)
 

The formula used assumes that the supplied mean value is the weighted arithmetic mean of the sample data, not a known population parameter. This method is supplied only to save computation when the mean has already been computed.

This formula will not return the same result as the unweighted variance when all weights are equal, unless all weights are equal to 1. The formula assumes that weights are to be treated as "expansion values," as will be the case if for example the weights represent frequency counts. To normalize weights so that the denominator in the variance computation equals the length of the input vector minus one, use

   evaluate(values, MathArrays.normalizeArray(weights, values.length), mean); 
 

Returns 0 for a single-value (i.e. length = 1) sample.

Throws MathIllegalArgumentException if any of the following are true:

• the values array is null
• the weights array is null
• the weights array does not have the same length as the values array
• the weights array contains one or more infinite values
• the weights array contains one or more NaN values
• the weights array contains negative values

Does not change the internal state of the statistic.

Parameters:

values - the input array

weights - the weights array

mean - the precomputed weighted mean value

Returns:

the variance of the values or Double.NaN if length = 0

Throws:

MathIllegalArgumentException - if the parameters are not valid

Since:

2.1

isBiasCorrected

public boolean isBiasCorrected()

Returns:

Returns the isBiasCorrected.

setBiasCorrected

public void setBiasCorrected(boolean biasCorrected)

Parameters:

biasCorrected - The isBiasCorrected to set.

copy

public Variance copy()

Returns a copy of the statistic with the same internal state.

Specified by:

copy in interface StorelessUnivariateStatistic

Specified by:

copy in interface UnivariateStatistic

Specified by:

copy in class AbstractStorelessUnivariateStatistic

Returns:

a copy of the statistic

copy

public static void copy(Variance source,
        Variance dest)

Copies source to dest.

Neither source nor dest can be null.

Parameters:

source - Variance to copy

dest - Variance to copy to

Throws:

NullArgumentException - if either source or dest is null