StatWeibullPlot Routine

Summary

Constructs the Weibull Probability Chart.

Declaration

Procedure StatWeibullPlot(Data: TVec; XDrawVec, YDrawVec: TVec; out MinX, MaxX, MinY, MaxY: TSample; 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 Weibull Probability Chart. Use TStatProbSeries to visualize/plot constructed values. The Weibull plot is a graphical technique for determining if a data set comes from a population that would logically be fit by a 2-parameter Weibull distribution (the location is assumed to be zero).

The Weibull plot has special scales that are designed so that if the data do in fact follow a Weibull distribution, the points will be linear (or nearly linear). The least squares fit of this line yields estimates for the shape and scale parameters of the Weibull distribution. Weibull distribution (the location is assumed to be zero).

The Weibull plot can be used to answer the following questions:

Do the data follow a 2-parameter Weibull distribution?
What is the best estimate of the shape parameter for the 2-parameter Weibull distribution?
What is the best estimate of the scale (= variation) parameter for the 2-parameter Weibull distribution?

See Also
TStatProbSeries

Example 1

  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);
    RandomWeibull(3,1.2,Data);
    StatWeibullPlot(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);
    RandomWeibull(3, 1.2, data);
    StatWeibullPlot(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.RandomWeibull(3.0, 1.2); // some random values
      StatProbPlots.StatWeibullPlot(data, xvec, yvec, out x1, out x2, out y1, out y2, false);
      Series1.MinX = x1;
      Series1.MaxX = x2;
      Series1.MinY = y1;
      Series1.MaxY = y2;
      MtxVecTee.DrawValues(xvec,yvec,Series1,false);
    }
  }