org.apache.commons.math3.stat.descriptive.moment

## Class Variance

• All Implemented Interfaces:
Serializable, StorelessUnivariateStatistic, UnivariateStatistic, WeightedEvaluation, MathArrays.Function

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.

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 isBiasCorrected)
Constructs a Variance with the specified isBiasCorrected property
Variance(boolean isBiasCorrected, 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)
• ### 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 isBiasCorrected)
Constructs a Variance with the specified isBiasCorrected property
Parameters:
isBiasCorrected - setting for bias correction - true means bias will be corrected and is equivalent to using the argumentless constructor
• #### Variance

public Variance(boolean isBiasCorrected,
SecondMoment m2)
Constructs a Variance with the specified isBiasCorrected property and the supplied external second moment.
Parameters:
isBiasCorrected - setting for bias correction - true means bias will be corrected
m2 - the SecondMoment (Third or Fourth moments work here as well.)
• ### 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.
• #### getN

public long getN()
Returns the number of values that have been added.
Specified by:
getN in interface StorelessUnivariateStatistic
Returns:
the number of values.
• #### evaluate

public double evaluate(double[] values,
int begin,
int length)
throws MathIllegalArgumentException
Returns the variance of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty. Note that Double.NaN may also be returned if the input includes NaN and / or infinite values.

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

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

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)
throws MathIllegalArgumentException

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)
throws MathIllegalArgumentException
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)
throws MathIllegalArgumentException
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)
throws MathIllegalArgumentException
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)
throws MathIllegalArgumentException

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.