Moment Routine

Summary

Moments.

Declaration

Function Moment(X: TVec; AMean: TSample; const AOrder: Integer): TSample;

Parameter	Description
X	Data. An exception is raised if X vector is complex.
AMean	A mean value of all X vector elements.
AOrder	Defines the order of central moment.

Result

the AOrder-th central moment of all X vector elements.

Example 1

Calculate the fourth moment (related to Kurtosis)

  Uses MtxExpr, Statistics, Math387;
  procedure Example;
  var a: Vector;
    AMean,
    M4 : TSample;
  begin
    a.SetIt(false,[1, 2, 7, 8]);
    AMean := a.Mean;
    M4 := Moment(a,AMean,4); // M4 = 94.5625
  end;

  #include "MtxVecCpp.h"
  #include "Statistics.hpp"
  void __fastcall Example();
  {
    Vector a;
    a->SetIt(false, OPENARRAY(double,(1, 2, 7, 8)));
    double amean = a->Mean();
    double m4 = Moment(a,amean,4);
    // m4 = 94.5625
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector a = new Vector(0),
      a.SetIt(false, new double[] {1, 2, 7, 8});
      double amean = a.Mean();
      double m4 = Statistics.Moment(a,amean,4);
      // m4 = 94.5625
    }
  }