StatNormalPlot Routine

Summary

Constructs the Normal Probability Chart.

Declaration

Procedure StatNormalPlot(Data: TVec; XDrawVec, YDrawVec: TVec; out MinX, MaxX, MinY, MaxY: TSample; StdErrs: TVec = nil; DataSorted: boolean = true);

Parameter	Description
Data	Data to be drawn.
DataSorted	If true, algorithm assumes Data is already sorted in ascending order. If Data is not sorted, you must set this parameter to false so that internal algorithm will automatically do the sorting.
XDrawVec	Retunrs vector of X values to be drawn.
YDrawVec	Returns vector of Y values to be drawn.
minX,minY	Returns slope line start point. These value are used by TStatProbSeries series.
maxX,maxY	Returns slope line end point. These value are used by TStatProbSeries series.

Description

Constructs the Normal Probability Chart. Use TStatProbSeries to visualize/plot constructed values. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line. Departures from this straight line indicate departures from normality.

The normal probability plot is used to answer the following questions:

Are the data normally distributed?
What is the nature of the departure from normality (data skewed, shorter than expected tails, longer than expected tails)?

See Also
TStatProbSeries
TStatProbSeries

Example 1

The following code will create probability plot and then plot calculated values.

  Uses MtxExpr, StatProbPlots, StatSeries, Math387, MtxVecTee;
  procedure Example(Series1: TStatProbSeries);
  var Data, XVec, YVec: Vector;
    X1,Y1,X2,Y2: TSample;
  begin
    // generate some random values for Data vec
    Data.Size(100);
    Data.RandGauss(0.0,1.0); // standard norm. dist.
    StatNormalPlot(Data,XVec,YVec,X1,X2,Y1,Y2,false);
    With Series1 do
    begin
      MinX := X1;
      MinY := Y1;
      MaxX := X2;
      MaxY := Y2;
    end;
    DrawValues(XVec,YVec,Series1);
  end;

  #include "Math387.hpp"
  #include "MtxVecCpp.h"
  #include "StatProbPlots.hpp"
  #include "StatSeries.hpp"
  #include "MtxVecTee.hpp"
  void __fastcall Example(TStatProbSeries * Series1);
  {
    Vector data,xvec,yvec;
    double x1,x2,y1,y2;

    data->Size(100,false);
    data->RandGauss(0.0,1.0) // standard distribution
    StatNormalPlot(data,xvec,yvec,x1,x2,y1,y2,false);
    Series1->MinX = x1;
    Series1->MaxX = x2;
    Series1->MinY = y1;
    Series1->MaxY = y2;
    DrawValues(xvec,yvec,Series1);
  }

  using Dew.Math;
  using Dew.Math.Units;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example(ProbabilityPlot Series1)
    {
      double x1,x2;
      double y1,y2;

      Vector data = new Vector(100,false);
      Vector xvec = new Vector(0);
      Vector yvec = new Vector(0);

      data.RandGauss(0.0, 1.0); // standard distribution
      StatProbPlots.StatNormalPlot(data, xvec, yvec, out x1, out x2, out y1, out y2, null,false);
      Series1.MinX = x1;
      Series1.MaxX = x2;
      Series1.MinY = y1;
      Series1.MaxY = y2;
      MtxVecTee.DrawValues(xvec,yvec,Series1,false);
    }
  }