Package org.hipparchus.stat.descriptive.moment

Class Kurtosis

java.lang.Object

org.hipparchus.stat.descriptive.AbstractStorelessUnivariateStatistic

org.hipparchus.stat.descriptive.moment.Kurtosis

All Implemented Interfaces:

Serializable, DoubleConsumer, 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	Description
protected final boolean	incMoment	Determines whether or not this statistic can be incremented or cleared.
protected final org.hipparchus.stat.descriptive.moment.FourthMoment	moment	Fourth Moment on which this statistic is based

Constructor Summary

Constructors

Constructor	Description
Kurtosis()	Construct a Kurtosis.
Kurtosis(org.hipparchus.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

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.
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.hipparchus.stat.descriptive.AbstractStorelessUnivariateStatistic

equals, hashCode, toString

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.util.function.DoubleConsumer

andThen

Methods inherited from interface org.hipparchus.stat.descriptive.StorelessUnivariateStatistic

accept, incrementAll, incrementAll

Methods inherited from interface org.hipparchus.stat.descriptive.UnivariateStatistic

evaluate

Field Details

moment

protected final org.hipparchus.stat.descriptive.moment.FourthMoment moment

Fourth Moment on which this statistic is based

incMoment

protected final 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 Details

Kurtosis

public Kurtosis()

Construct a Kurtosis.

Kurtosis

public Kurtosis(org.hipparchus.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 Details

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 MathArrays.Function

Specified by:

evaluate in interface StorelessUnivariateStatistic

Specified by:

evaluate in interface UnivariateStatistic

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