StatProbPlots.StatNormalPlot Method

void StatNormalPlot(TVec Data, TVec XDrawVec, TVec YDrawVec, ref Double MinX, ref Double MaxX, ref Double MinY, ref Double MaxY, TVec StdErrs, Boolean DataSorted)

Constructs the Normal Probability Chart.

#	Name	Description
1	Data	Data to be drawn. The assumption is data values are sorted.
2	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.
3	XDrawVec	Returns normal probability plot horizontal values to be drawn - > estimated quantiles from Data vector or in this case sorted Data values.
4	YDrawVec	Returns normal probability plot vertical values to be drawn - > Values are generated from theoretical standard normal distribution with parameters mu=0, sigma^2=1.
5	MinX	Returns slope line start X point, XDrawVec 25th percentile. These value are used by Dew.Stats.Tee.ProbabilityPlot series.
6	MinY	Returns slope line start Y point, YDrawVec 25th percentile. These value are used by Dew.Stats.Tee.ProbabilityPlot series.
7	MaxX	Returns slope line end X point, XDrawVec 75th percentile. These value are used by Dew.Stats.Tee.ProbabilityPlot series.
8	MaxY	Returns slope line end Y point, YDrawVec 75th percentile. These value are used by Dew.Stats.Tee.ProbabilityPlot series.
9	StdErrs	Standard error

Result: stored in self (calling object)

Remarks:

How to construct Normal distribution probability plot?

If needed, Data values are sorted (DataSorted parameter must be set to false).
Abscissa drawing values are formed by estimated data quantiles - ordered Data values. After calculation they are copied to XDrawVec. Dew.Math.TMtxVecBase.Length and Dew.Math.TMtxVec.Complex properties of XDrawVec are adjusted automatically.
Ordinate drawing values are formed by using theoretical probability p i.e the so Z values. After calculation they are copied to YDrawVec. Dew.Math.TMtxVecBase.Length and Dew.Math.TMtxVec.Complex properties of YDrawVec are adjusted automatically.
XDrawVec and YDrawVec 25th and 75th percentile points are used to construct a reference line. Drawing points 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)?

Examples

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);
    }
}

See Also: ProbabilityPlot