Class Kurtosis
- All Implemented Interfaces:
Serializable
,DoubleConsumer
,StorelessUnivariateStatistic
,UnivariateStatistic
,MathArrays.Function
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:
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Field Summary
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Constructor Summary
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Method Summary
Modifier and TypeMethodDescriptionvoid
clear()
Clears the internal state of the Statisticcopy()
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
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
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Field Details
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moment
protected final org.hipparchus.stat.descriptive.moment.FourthMoment momentFourth Moment on which this statistic is based -
incMoment
protected final boolean incMomentDetermines whether or not this statistic can be incremented or cleared.Statistics based on (constructed from) external moments cannot be incremented or cleared.
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Constructor Details
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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
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Kurtosis
Copy constructor, creates a newKurtosis
identical to theoriginal
.- Parameters:
original
- theKurtosis
instance to copy- Throws:
NullArgumentException
- if original is null
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Method Details
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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 interfaceStorelessUnivariateStatistic
- Specified by:
increment
in classAbstractStorelessUnivariateStatistic
- Parameters:
d
- the new value.
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getResult
public double getResult()Returns the current value of the Statistic.- Specified by:
getResult
in interfaceStorelessUnivariateStatistic
- Specified by:
getResult
in classAbstractStorelessUnivariateStatistic
- Returns:
- value of the statistic,
Double.NaN
if it has been cleared or just instantiated.
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clear
public void clear()Clears the internal state of the Statistic- Specified by:
clear
in interfaceStorelessUnivariateStatistic
- Specified by:
clear
in classAbstractStorelessUnivariateStatistic
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getN
public long getN()Returns the number of values that have been added.- Specified by:
getN
in interfaceStorelessUnivariateStatistic
- Returns:
- the number of values.
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evaluate
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 interfaceMathArrays.Function
- Specified by:
evaluate
in interfaceStorelessUnivariateStatistic
- Specified by:
evaluate
in interfaceUnivariateStatistic
- Parameters:
values
- the input arraybegin
- index of the first array element to includelength
- 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:
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copy
Returns a copy of the statistic with the same internal state.- Specified by:
copy
in interfaceStorelessUnivariateStatistic
- Specified by:
copy
in interfaceUnivariateStatistic
- Specified by:
copy
in classAbstractStorelessUnivariateStatistic
- Returns:
- a copy of the statistic
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