java.lang.Object
- org.apache.commons.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic
- - org.apache.commons.math4.legacy.stat.descriptive.moment.Kurtosis

All Implemented Interfaces:

MathArrays.Function, 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 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.

Field Summary

Fields
Modifier and Type	Field	Description
`protected boolean`	`incMoment`	Determines whether or not this statistic can be incremented or cleared.
`protected org.apache.commons.math4.legacy.stat.descriptive.moment.FourthMoment`	`moment`	Fourth Moment on which this statistic is based.

Constructor Summary

Constructors
Constructor	Description
`Kurtosis()`	Construct a Kurtosis.
`Kurtosis(org.apache.commons.math4.legacy.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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	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.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic
equals, evaluate, hashCode, incrementAll, incrementAll

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - moment
```
protected org.apache.commons.math4.legacy.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.math4.legacy.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.
    
    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 MathArrays.Function
    
    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:
    
    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

Class Kurtosis

Field Summary

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic

Methods inherited from class java.lang.Object

Field Detail

moment

incMoment

Constructor Detail

Kurtosis

Kurtosis

Kurtosis

Method Detail

increment

getResult

clear

getN

evaluate

copy

copy