Vector.Kurtosis Method

Vector Class

Double Kurtosis(Double AMean, Double AStdDev)

The Kurtosis (fourth central momentum).

#NameTypeDescription
1AMeanDoublepre-computed mean
2AStdDevDoubleoutput std deviation

Returns: Double

Remarks:

Calculate the calling object kurtosis by using mean value AMean and standard deviation AStdDev. Kurtosis is the fourth central moment, divided by fourth power of standard deviation:

Kurtosis=1σ4∑k=0Length−1(V[k]−⟨V⟩)4,where ⟨V⟩=mean value\text{Kurtosis}=\frac{1}{\sigma ^4} \sum _{k=0} ^{\text{Length}-1}\left( V[k] -\langle V\rangle \right)^4 ,\quad \text{where } \langle V \rangle = \text{mean value}
See Also: Vector.Skewness, Vector.Mean, Vector.StdDev

Indexed: Double Kurtosis(Double AMean, Double AStdDev, Int32 Index, Int32 Len)

Calculate the kurtosis for elements [Index]..[Index+Len-1].

#NameTypeDescription
1AMeanDoublepre-computed mean
2AStdDevDoubleoutput std deviation
3IndexInt32start index
4LenInt32element count

Returns: Double

Remarks:

An exception is raised if Dew.Math.Vector.ConditionCheck is True and array borders are overrun. The AMean and AStdDev passed as parameters must be computed from the same elements (Index, Len) as the Kurtosis itself.