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

    java.lang.Object
      org.apache.commons.math.stat.descriptive.AbstractUnivariateStatistic
          org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic
              org.apache.commons.math.stat.descriptive.moment.Kurtosis

All Implemented Interfaces:
  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: 1.1 $ $Date: 2004/10/08 05:08:17 $
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
`(package 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

    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`
  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`
  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:
    `IllegalArgumentException` - if the input array is null or the array index parameters are not valid
  See Also:
    `UnivariateStatistic.evaluate(double[], int, int)`

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Copyright © 2003-2004 The Apache Software Foundation. All Rights Reserved.