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

## Class Kurtosis

- java.lang.Object
- - org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic
  - - org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic
    - - 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 Double.NaN may also be returned if the input includes NaN and / or infinite values.

  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:
    Serialized Form

- - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `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

    Constructors
    Constructor and Description
    `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

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `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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