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

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

public class Kurtosis
extends AbstractStorelessUnivariateStatistic

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:
$Revision: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $
See Also:
Serialized Form

Field Summary
protected  boolean incMoment
          Determines whether or not this statistic can be incremented or cleared.
protected  FourthMoment moment
          Fourth Moment on which this statistic is based
private static long serialVersionUID
          Serializable version identifier
 
Constructor Summary
Kurtosis()
          Construct a Kurtosis
Kurtosis(FourthMoment m4)
          Construct a Kurtosis from an external moment
 
Method Summary
 void clear()
          Clears the internal state of the Statistic
 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.math.stat.descriptive.AbstractStorelessUnivariateStatistic
equals, evaluate, hashCode, incrementAll, incrementAll
 
Methods inherited from class org.apache.commons.math.stat.descriptive.AbstractUnivariateStatistic
test
 
Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

serialVersionUID

private static final long serialVersionUID
Serializable version identifier

See Also:
Constant Field Values

moment

protected 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(FourthMoment m4)
Construct a Kurtosis from an external moment

Parameters:
m4 - external Moment
Method Detail

increment

public void increment(double d)
Description copied from interface: StorelessUnivariateStatistic
Updates the internal state of the statistic to reflect the addition of the new value.

Specified by:
increment in interface StorelessUnivariateStatistic
Specified by:
increment in class AbstractStorelessUnivariateStatistic
Parameters:
d - the new value.
See Also:
StorelessUnivariateStatistic.increment(double)

getResult

public double getResult()
Description copied from interface: StorelessUnivariateStatistic
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.
See Also:
StorelessUnivariateStatistic.getResult()

clear

public void clear()
Description copied from interface: StorelessUnivariateStatistic
Clears the internal state of the Statistic

Specified by:
clear in interface StorelessUnivariateStatistic
Specified by:
clear in class AbstractStorelessUnivariateStatistic
See Also:
StorelessUnivariateStatistic.clear()

getN

public long getN()
Description copied from interface: StorelessUnivariateStatistic
Returns the number of values that have been added.

Returns:
the number of values.
See Also:
StorelessUnivariateStatistic.getN()

evaluate

public double evaluate(double[] values,
                       int begin,
                       int length)
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
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:
java.lang.IllegalArgumentException - if the input array is null or the array index parameters are not valid
See Also:
UnivariateStatistic.evaluate(double[], int, int)