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

## Class Skewness

- java.lang.Object
- - org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic
  - - org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic
    - - org.apache.commons.math3.stat.descriptive.moment.Skewness

- All Implemented Interfaces:
    Serializable, StorelessUnivariateStatistic, UnivariateStatistic, MathArrays.Function

      public class Skewness
      extends AbstractStorelessUnivariateStatistic
      implements Serializable

  Computes the skewness of the available values.

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

  skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^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 < 3. `Double.Nan` is returned when there is not sufficient data to compute the statistic. 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.ThirdMoment` | `moment` Third moment on which this statistic is based

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `Skewness()` Constructs a Skewness
    `Skewness(Skewness original)` Copy constructor, creates a new `Skewness` identical to the `original`
    `Skewness(org.apache.commons.math3.stat.descriptive.moment.ThirdMoment m3)` Constructs a Skewness with an external moment

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `void` | `clear()` Clears the internal state of the Statistic
    `Skewness` | `copy()` Returns a copy of the statistic with the same internal state.
    `static void` | `copy(Skewness source, Skewness dest)` Copies source to dest.
    `double` | `evaluate(double[] values, int begin, int length)` Returns the Skewness of the entries in the specifed portion of the input array.
    `long` | `getN()` Returns the number of values that have been added.
    `double` | `getResult()` Returns the value of the statistic based on the values that have been added.
    `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.ThirdMoment moment

      Third 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

    - #### Skewness

          public Skewness()

      Constructs a Skewness

    - #### Skewness

          public Skewness(org.apache.commons.math3.stat.descriptive.moment.ThirdMoment m3)

      Constructs a Skewness with an external moment
      Parameters:
        `m3` - external moment

    - #### Skewness

          public Skewness(Skewness original)
                   throws NullArgumentException

      Copy constructor, creates a new `Skewness` identical to the `original`
      Parameters:
        `original` - the `Skewness` 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 `Skewness(ThirdMoment)` is used to create a Skewness, this method does nothing. In that case, the ThirdMoment 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 value of the statistic based on the values that have been added.

      See `Skewness` for the definition used in the computation.

      Specified by:
        `getResult` in interface `StorelessUnivariateStatistic`
      Specified by:
        `getResult` in class `AbstractStorelessUnivariateStatistic`
      Returns:
        the skewness of the available values.

    - #### getN

          public long getN()

      Returns the number of values that have been added.
      Specified by:
        `getN` in interface `StorelessUnivariateStatistic`
      Returns:
        the number of values.

    - #### clear

          public void clear()

      Clears the internal state of the Statistic
      Specified by:
        `clear` in interface `StorelessUnivariateStatistic`
      Specified by:
        `clear` in class `AbstractStorelessUnivariateStatistic`

    - #### evaluate

          public double evaluate(double[] values,
                        int begin,
                        int length)
                          throws MathIllegalArgumentException

      Returns the Skewness of the entries in the specifed portion of the input array.

      See `Skewness` for the definition used in the computation.

      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` - the index of the first array element to include
        `length` - the number of elements to include
      Returns:
        the skewness of the values or Double.NaN if length is less than 3
      Throws:
        `MathIllegalArgumentException` - if the array is null or the array index parameters are not valid
      See Also:
        `UnivariateStatistic.evaluate(double[], int, int)`

    - #### copy

          public Skewness 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(Skewness source,
                  Skewness dest)
                           throws NullArgumentException

      Copies source to dest.

      Neither source nor dest can be null.

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

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