Vector.Kurtosis Method

Vector Class

function Kurtosis(AMean: Double; AStdDev: Double): Double;

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: function Kurtosis(AMean: Double; AStdDev: Double; Index: Integer; Len: Integer): Double;

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

#NameTypeDescription
1AMeanDoublepre-computed mean
2AStdDevDoubleoutput std deviation
3IndexIntegerstart index
4LenIntegerelement count

Returns: Double

Remarks:

An exception is raised if 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.