Matrix.Skewness Method

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

Skewness (third central momentum).

#	Name	Type	Description
1	AMean	Double	pre-computed mean
2	AStdDev	Double	output std deviation

Returns: Double

Remarks:

Calculate the calling object skewness by using mean value AMean and standard deviation AStdDev. Skewness is the third central moment, divided by third power of standard deviation:

\text{Skewness}=\frac{1}{\sigma ^3} \sum _{k=0} ^{\text{Length}-1}\left( V[k] -\langle V\rangle \right)^3 ,\quad \text{where } \langle V \rangle = \text{mean value}

Examples

var a: Matrix;
    c,d: double;
begin
    a.SetIt(1,4,False,[1,2,3,4]);
    d := a.Mean;
    c := a.Skewness(d, a.StdDev(d)); //or

    d := Mean(a);
    c := Skewness(a, d, StdDev(a, d));
end;

See Also: Matrix.Kurtosis, Matrix.Mean, Matrix.StdDev

Indexed: function Skewness(AMean: Double; AStdDev: Double; Index: Integer; Len: Integer): Double;

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

#	Name	Type	Description
1	AMean	Double	pre-computed mean
2	AStdDev	Double	output std deviation
3	Index	Integer	start index
4	Len	Integer	element count

Returns: Double

Remarks:

An exception is raised if Matrix.ConditionCheck is True and array borders are overrun. The AMean and AStdDev parameters must be computed from the same elements from which the Skewness is to be computed.