Class LongVariance
- java.lang.Object
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- org.apache.commons.statistics.descriptive.LongVariance
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- All Implemented Interfaces:
java.util.function.DoubleSupplier
,java.util.function.IntSupplier
,java.util.function.LongConsumer
,java.util.function.LongSupplier
,LongStatistic
,StatisticAccumulator<LongVariance>
,StatisticResult
public final class LongVariance extends java.lang.Object implements LongStatistic, StatisticAccumulator<LongVariance>
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
NaN
if no values are added. - The result is zero if there is one 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
biased
option is enabled the normalisation factor is changed to \( \frac{1}{n} \) for a biased estimator of the sample variance.The implementation uses an exact integer sum to compute the scaled (by \( n \)) sum of squared deviations from the mean; this is normalised by the scaled correction factor.
\[ \frac {n \times \sum_{i=1}^n x_i^2 - (\sum_{i=1}^n x_i)^2}{n \times (n - 1)} \]
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.
This implementation is not thread safe. If multiple threads access an instance of this class concurrently, and at least one of the threads invokes the
accept
orcombine
method, it must be synchronized externally.However, it is safe to use
accept
andcombine
asaccumulator
andcombiner
functions ofCollector
on a parallel stream, because the parallel implementation ofStream.collect()
provides the necessary partitioning, isolation, and merging of results for safe and efficient parallel execution.- Since:
- 1.1
- See Also:
- variance (Wikipedia), Algorithms for computing the variance (Wikipedia), Bessel's correction
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Constructor Summary
Constructors Modifier Constructor Description private
LongVariance()
Create an instance.private
LongVariance(UInt192 sumSq, Int128 sum, int n)
Create an instance.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description void
accept(long value)
Updates the state of the statistic to reflect the addition ofvalue
.LongVariance
combine(LongVariance other)
Combines the state of theother
statistic into this one.(package private) double
computeMean()
Compute the mean.private static double
computeSSDevN(UInt192 sumSq, Int128 sum, long n)
Compute the sum-of-squared deviations multiplied by the count of values:n * sum(x^2) - sum(x)^2
.(package private) double
computeSumOfSquaredDeviations()
Compute the sum of the squared deviations from the mean.(package private) static double
computeVarianceOrStd(UInt192 sumSq, Int128 sum, long n, boolean biased, boolean std)
Compute the variance (or standard deviation).static LongVariance
create()
Creates an instance.double
getAsDouble()
Gets the variance of all input values.static LongVariance
of(long... values)
Returns an instance populated using the inputvalues
.LongVariance
setBiased(boolean v)
Sets the value of the biased flag.private static java.math.BigInteger
square(java.math.BigInteger x)
Convenience method to square a BigInteger.-
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 org.apache.commons.statistics.descriptive.StatisticResult
getAsBigInteger, getAsInt, getAsLong
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Method Detail
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create
public static LongVariance create()
Creates an instance.The initial result is
NaN
.- Returns:
LongVariance
instance.
-
of
public static LongVariance of(long... values)
Returns an instance populated using the inputvalues
.- Parameters:
values
- Values.- Returns:
LongVariance
instance.
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accept
public void accept(long value)
Updates the state of the statistic to reflect the addition ofvalue
.- Specified by:
accept
in interfacejava.util.function.LongConsumer
- 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:
getAsDouble
in interfacejava.util.function.DoubleSupplier
- Returns:
- variance of all values.
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computeVarianceOrStd
static double computeVarianceOrStd(UInt192 sumSq, Int128 sum, long n, boolean biased, boolean std)
Compute the variance (or standard deviation).The
std
flag controls if the result is returned as the standard deviation using thesquare root
function.- Parameters:
sumSq
- Sum of the squared values.sum
- Sum of the values.n
- Count of values that have been added.biased
- Flag to control if the statistic is biased, or should use a bias correction.std
- Flag to control if the statistic is the standard deviation.- Returns:
- the variance (or standard deviation)
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computeSSDevN
private static double computeSSDevN(UInt192 sumSq, Int128 sum, long n)
Compute the sum-of-squared deviations multiplied by the count of values:n * sum(x^2) - sum(x)^2
.- Parameters:
sumSq
- Sum of the squared values.sum
- Sum of the values.n
- Count of values that have been added.- Returns:
- the sum-of-squared deviations precursor
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computeSumOfSquaredDeviations
double computeSumOfSquaredDeviations()
Compute the sum of the squared deviations from the mean.This is a helper method used in higher order moments.
- Returns:
- the sum of the squared deviations
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computeMean
double computeMean()
Compute the mean.This is a helper method used in higher order moments.
- Returns:
- the mean
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square
private static java.math.BigInteger square(java.math.BigInteger x)
Convenience method to square a BigInteger.- Parameters:
x
- Value- Returns:
- x^2
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combine
public LongVariance combine(LongVariance other)
Description copied from interface:StatisticAccumulator
Combines the state of theother
statistic into this one.- Specified by:
combine
in interfaceStatisticAccumulator<LongVariance>
- Parameters:
other
- Another statistic to be combined.- Returns:
this
instance after combiningother
.
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setBiased
public LongVariance setBiased(boolean v)
Sets the value of the biased flag. The default value isfalse
.If
false
the sum of squared deviations from the sample mean is normalised byn - 1
wheren
is the number of samples. This is Bessel's correction for an unbiased estimator of the variance of a hypothetical infinite population.If
true
the sum of squared deviations is normalised by the number of samplesn
.Note: This option only applies when
n > 1
. The variance ofn = 1
is 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
combine
operation.- Parameters:
v
- Value.- Returns:
this
instance
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