Class Variance
 All Implemented Interfaces:
Serializable
,DoubleConsumer
,AggregatableStatistic<Variance>
,StorelessUnivariateStatistic
,UnivariateStatistic
,WeightedEvaluation
,MathArrays.Function
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. 526531.  The
evaluate
methods leverage the fact that they have the full array of values in memory to execute a twopass algorithm. Specifically, these methods use the "corrected twopass algorithm" from Chan, Golub, Levesque, Algorithms for Computing the Sample Variance, American Statistician, vol. 37, no. 3 (1983) pp. 242247.
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:

Field Summary
Modifier and TypeFieldDescriptionprotected final boolean
Whether or notincrement(double)
should increment the internal second moment.protected final SecondMoment
SecondMoment is used in incremental calculation of Variance 
Constructor Summary
ConstructorDescriptionVariance()
Constructs a Variance with default (true)isBiasCorrected
property.Variance
(boolean isBiasCorrected) Constructs a Variance with the specifiedisBiasCorrected
property.Variance
(boolean isBiasCorrected, SecondMoment m2) Constructs a Variance with the specifiedisBiasCorrected
property and the supplied external second moment.Variance
(SecondMoment m2) Constructs a Variance based on an external second moment.Copy constructor, creates a newVariance
identical to theoriginal
. 
Method Summary
Modifier and TypeMethodDescriptionvoid
Aggregates the provided instance into this instance.void
clear()
Clears the internal state of the Statisticcopy()
Returns a copy of the statistic with the same internal state.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, 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, orDouble.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, orDouble.NaN
if the designated subarray is empty.long
getN()
Returns the number of values that have been added.double
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
Check if bias is corrected.withBiasCorrection
(boolean biasCorrection) Returns a new copy of this variance with the given bias correction setting.Methods inherited from class org.hipparchus.stat.descriptive.AbstractStorelessUnivariateStatistic
equals, hashCode, toString
Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface org.hipparchus.stat.descriptive.AggregatableStatistic
aggregate, aggregate
Methods inherited from interface java.util.function.DoubleConsumer
andThen
Methods inherited from interface org.hipparchus.stat.descriptive.StorelessUnivariateStatistic
accept, incrementAll, incrementAll
Methods inherited from interface org.hipparchus.stat.descriptive.UnivariateStatistic
evaluate
Methods inherited from interface org.hipparchus.stat.descriptive.WeightedEvaluation
evaluate

Field Details

moment
SecondMoment is used in incremental calculation of Variance 
incMoment
protected final boolean incMomentWhether or notincrement(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 Details

Variance
public Variance()Constructs a Variance with default (true)isBiasCorrected
property. 
Variance
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; whereasm2.increment(value)
increments bothm2
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 specifiedisBiasCorrected
property. Parameters:
isBiasCorrected
 setting for bias correction  true means bias will be corrected and is equivalent to using the argumentless constructor

Variance
Constructs a Variance with the specifiedisBiasCorrected
property and the supplied external second moment. Parameters:
isBiasCorrected
 setting for bias correction  true means bias will be correctedm2
 the SecondMoment (Third or Fourth moments work here as well.)

Variance
Copy constructor, creates a newVariance
identical to theoriginal
. Parameters:
original
 theVariance
instance to copy Throws:
NullArgumentException
 if original is null


Method Details

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
UnivariateStatistic.evaluate(double[])
rather than adding values one at a time using this method and then executinggetResult()
, sinceevaluate
leverages the fact that is has the full list of values together to execute a twopass algorithm. SeeVariance
.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 interfaceStorelessUnivariateStatistic
 Specified by:
increment
in classAbstractStorelessUnivariateStatistic
 Parameters:
d
 the new value.

getResult
public double getResult()Returns the current value of the Statistic. Specified by:
getResult
in interfaceStorelessUnivariateStatistic
 Specified by:
getResult
in classAbstractStorelessUnivariateStatistic
 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 interfaceStorelessUnivariateStatistic
 Returns:
 the number of values.

clear
public void clear()Clears the internal state of the Statistic Specified by:
clear
in interfaceStorelessUnivariateStatistic
 Specified by:
clear
in classAbstractStorelessUnivariateStatistic

aggregate
Aggregates the provided instance into this instance.This method can be used to combine statistics computed over partitions or subsamples  i.e., the value of this instance after this operation should be the same as if a single statistic would have been applied over the combined dataset.
 Specified by:
aggregate
in interfaceAggregatableStatistic<Variance>
 Parameters:
other
 the instance to aggregate into this instance

evaluate
Returns the variance of the entries in the specified portion of the input array, orDouble.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 singlevalue (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 interfaceMathArrays.Function
 Specified by:
evaluate
in interfaceStorelessUnivariateStatistic
 Specified by:
evaluate
in interfaceUnivariateStatistic
 Parameters:
values
 the input arraybegin
 index of the first array element to includelength
 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:

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, orDouble.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 singlevalue (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.
 Specified by:
evaluate
in interfaceWeightedEvaluation
 Parameters:
values
 the input arrayweights
 the weights arraybegin
 index of the first array element to includelength
 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

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. ReturnsDouble.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 singlevalue (i.e. length = 1) sample.
Does not change the internal state of the statistic.
 Parameters:
values
 the input arraymean
 the precomputed mean valuebegin
 index of the first array element to includelength
 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
Returns the variance of the entries in the input array, using the precomputed mean value. ReturnsDouble.NaN
if the array is empty.See
Variance
for details on the computing algorithm.If
isBiasCorrected
istrue
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, setisBiasCorrected
tofalse
before invoking this method.Returns 0 for a singlevalue (i.e. length = 1) sample.
Does not change the internal state of the statistic.
 Parameters:
values
 the input arraymean
 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. ReturnsDouble.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 singlevalue (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 arrayweights
 the weights arraymean
 the precomputed weighted mean valuebegin
 index of the first array element to includelength
 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

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 singlevalue (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 arrayweights
 the weights arraymean
 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

isBiasCorrected
public boolean isBiasCorrected()Check if bias is corrected. Returns:
 Returns the isBiasCorrected.

withBiasCorrection
Returns a new copy of this variance with the given bias correction setting. Parameters:
biasCorrection
 The bias correction flag to set. Returns:
 a copy of this instance with the given bias correction setting

copy
Returns a copy of the statistic with the same internal state. Specified by:
copy
in interfaceStorelessUnivariateStatistic
 Specified by:
copy
in interfaceUnivariateStatistic
 Specified by:
copy
in classAbstractStorelessUnivariateStatistic
 Returns:
 a copy of the statistic
