Class Variance
- java.lang.Object
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- org.apache.commons.statistics.descriptive.Variance
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- All Implemented Interfaces:
DoubleConsumer,DoubleSupplier,IntSupplier,LongSupplier,DoubleStatistic,StatisticAccumulator<Variance>,StatisticResult
public final class Variance extends Object implements DoubleStatistic, StatisticAccumulator<Variance>
Computes the variance of the available values. The default implementation uses the following definition of the sample variance:\[ \tfrac{1}{n-1} \sum_{i=1}^n (x_i-\overline{x})^2 \]
where \( \overline{x} \) is the sample mean, and \( n \) is the number of samples.
- The result is
NaNif no values are added. - The result is
NaNif any of the values isNaNor infinite. - The result is
NaNif the sum of the squared deviations from the mean is infinite. - The result is zero if there is one finite value in the data set.
The use of the term \( n − 1 \) is called Bessel's correction. This is an unbiased estimator of the variance of a hypothetical infinite population. If the
biasedoption is enabled the normalisation factor is changed to \( \frac{1}{n} \) for a biased estimator of the sample variance.The
accept(double)method uses a recursive updating algorithm based on West's algorithm (see Chan and Lewis (1979)).The
of(double...)method uses the corrected two-pass algorithm from Chan et al, (1983).Note that adding values using
acceptand then executinggetAsDoublewill sometimes give a different, less accurate, result than executingofwith the full array of values. The former approach should only be used when the full array of values is not available.Supports up to 263 (exclusive) observations. This implementation does not check for overflow of the count.
This class is designed to work with (though does not require) streams.
Note that this instance is not synchronized. If multiple threads access an instance of this class concurrently, and at least one of the threads invokes the
acceptorcombinemethod, it must be synchronized externally.However, it is safe to use
acceptandcombineasaccumulatorandcombinerfunctions ofCollectoron a parallel stream, because the parallel instance ofStream.collect()provides the necessary partitioning, isolation, and merging of results for safe and efficient parallel execution.References:
- Chan and Lewis (1979) Computing standard deviations: accuracy. Communications of the ACM, 22, 526-531. doi: 10.1145/359146.359152
- Chan, Golub and Levesque (1983) Algorithms for Computing the Sample Variance: Analysis and Recommendations. American Statistician, 37, 242-247. doi: 10.2307/2683386
- Since:
- 1.1
- See Also:
- Variance (Wikipedia),
Bessel's correction,
StandardDeviation
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description voidaccept(double value)Updates the state of the statistic to reflect the addition ofvalue.Variancecombine(Variance other)Combines the state of theotherstatistic into this one.static Variancecreate()Creates an instance.doublegetAsDouble()Gets the variance of all input values.static Varianceof(double... values)Returns an instance populated using the inputvalues.VariancesetBiased(boolean v)Sets the value of the biased flag.-
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface java.util.function.DoubleConsumer
andThen
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Methods inherited from interface org.apache.commons.statistics.descriptive.StatisticResult
getAsBigInteger, getAsInt, getAsLong
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Method Detail
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create
public static Variance create()
Creates an instance.The initial result is
NaN.- Returns:
Varianceinstance.
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of
public static Variance of(double... values)
Returns an instance populated using the inputvalues.Note:
Variancecomputed usingacceptmay be different from this variance.See
Variancefor details on the computing algorithm.- Parameters:
values- Values.- Returns:
Varianceinstance.
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accept
public void accept(double value)
Updates the state of the statistic to reflect the addition ofvalue.- Specified by:
acceptin interfaceDoubleConsumer- Parameters:
value- Value.
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getAsDouble
public double getAsDouble()
Gets the variance of all input values.When no values have been added, the result is
NaN.- Specified by:
getAsDoublein interfaceDoubleSupplier- Returns:
- variance of all values.
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combine
public Variance combine(Variance other)
Description copied from interface:StatisticAccumulatorCombines the state of theotherstatistic into this one.- Specified by:
combinein interfaceStatisticAccumulator<Variance>- Parameters:
other- Another statistic to be combined.- Returns:
thisinstance after combiningother.
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setBiased
public Variance setBiased(boolean v)
Sets the value of the biased flag. The default value isfalse.If
falsethe sum of squared deviations from the sample mean is normalised byn - 1wherenis the number of samples. This is Bessel's correction for an unbiased estimator of the variance of a hypothetical infinite population.If
truethe sum of squared deviations is normalised by the number of samplesn.Note: This option only applies when
n > 1. The variance ofn = 1is always 0.This flag only controls the final computation of the statistic. The value of this flag will not affect compatibility between instances during a
combineoperation.- Parameters:
v- Value.- Returns:
thisinstance
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