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

java.lang.Object
  extended by org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic
      extended by org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic
          extended by org.apache.commons.math3.stat.descriptive.moment.Kurtosis
All Implemented Interfaces:
Serializable, StorelessUnivariateStatistic, UnivariateStatistic, MathArrays.Function

public class Kurtosis
extends AbstractStorelessUnivariateStatistic
implements Serializable

Computes the Kurtosis of the available values.

We use the following (unbiased) formula to define kurtosis:

kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)]

where n is the number of values, mean is the Mean and std is the StandardDeviation

Note that this statistic is undefined for n < 4. Double.Nan is returned when there is not sufficient data to compute the statistic.

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.

Version:
$Id: Kurtosis.java 1416643 2012-12-03 19:37:14Z tn $
See Also:
Serialized Form

Field Summary
protected  boolean incMoment
          Determines whether or not this statistic can be incremented or cleared.
protected  org.apache.commons.math3.stat.descriptive.moment.FourthMoment moment
          Fourth Moment on which this statistic is based
 
Constructor Summary
Kurtosis()
          Construct a Kurtosis
Kurtosis(org.apache.commons.math3.stat.descriptive.moment.FourthMoment m4)
          Construct a Kurtosis from an external moment
Kurtosis(Kurtosis original)
          Copy constructor, creates a new Kurtosis identical to the original
 
Method Summary
 void clear()
          Clears the internal state of the Statistic
 Kurtosis copy()
          Returns a copy of the statistic with the same internal state.
static void copy(Kurtosis source, Kurtosis dest)
          Copies source to dest.
 double evaluate(double[] values, int begin, int length)
          Returns the kurtosis of the entries in the specified portion of the input array.
 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.
 
Methods inherited from class org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic
equals, evaluate, 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 org.apache.commons.math3.stat.descriptive.moment.FourthMoment moment
Fourth Moment on which this statistic is based


incMoment

protected boolean incMoment
Determines whether or not this statistic can be incremented or cleared.

Statistics based on (constructed from) external moments cannot be incremented or cleared.

Constructor Detail

Kurtosis

public Kurtosis()
Construct a Kurtosis


Kurtosis

public Kurtosis(org.apache.commons.math3.stat.descriptive.moment.FourthMoment m4)
Construct a Kurtosis from an external moment

Parameters:
m4 - external Moment

Kurtosis

public Kurtosis(Kurtosis original)
         throws NullArgumentException
Copy constructor, creates a new Kurtosis identical to the original

Parameters:
original - the Kurtosis 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.

Note that when Kurtosis(FourthMoment) is used to create a Variance, this method does nothing. In that case, the FourthMoment 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.

clear

public void clear()
Clears the internal state of the Statistic

Specified by:
clear in interface StorelessUnivariateStatistic
Specified by:
clear in class AbstractStorelessUnivariateStatistic

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 kurtosis of the entries in the specified portion of the input array.

See Kurtosis for details on the computing algorithm.

Throws IllegalArgumentException 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 kurtosis of the values or Double.NaN if length is less than 4
Throws:
MathIllegalArgumentException - if the input array is null or the array index parameters are not valid
See Also:
UnivariateStatistic.evaluate(double[], int, int)

copy

public Kurtosis 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(Kurtosis source,
                        Kurtosis dest)
                 throws NullArgumentException
Copies source to dest.

Neither source nor dest can be null.

Parameters:
source - Kurtosis to copy
dest - Kurtosis to copy to
Throws:
NullArgumentException - if either source or dest is null


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