Variance (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic
- - org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic
  - - org.apache.commons.math3.stat.descriptive.moment.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.
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 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)`

Methods inherited from class org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic
equals, hashCode, incrementAll, incrementAll

Methods inherited from class org.apache.commons.math3.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 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.)
  - Variance
```
public Variance(Variance original)
         throws NullArgumentException
```
    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)
                throws MathIllegalArgumentException
```
    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)
                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
    See Also:
    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.
  - 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)
                 throws NullArgumentException
```
    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

Class Variance

Field Summary

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic

Methods inherited from class org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic

Methods inherited from class java.lang.Object

Field Detail

moment

incMoment

Constructor Detail

Variance

Variance

Variance

Variance

Variance

Method Detail

increment

getResult

getN

clear

evaluate

evaluate

evaluate

evaluate

evaluate

evaluate

evaluate

evaluate

isBiasCorrected

setBiasCorrected

copy

copy