Statistics.ShapiroFrancia Function

The Shapiro-Francia test for normality of data.

Pascal

function ShapiroFrancia(const Data: TVec; out hRes: THypothesisResult; out Signif: double; hType: THypothesisType = htTwoTailed; Alpha: double = 0.05): double;

File

Statistics

Parameters

Parameters	Description
Data	Data vector, containing ordered and unique deviates from unknown distribution.
hRes	Returns the result of the null hypothesis (default assumption is that data comes from normal distribution).
Signif	(Significance level) returns the probability of observing the given result by chance given that the null hypothesis is true.
hType	Defines the type of the null hypothesis (left, right and two - tailed).
Alpha	Defines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected.

Returns

the Shapiro-Francia statistics.

Description

Performs the The Shapiro-Francia test for normality of data.

Notes

Basic assumption is Data values i.e. deviates from unknown distribution are ordered and unique.ž

See Also

Unique, ShapiroWilks

Example

In this example we'll use Shapiro-Francia test to determine if data is coming from normal distribution.

Uses MtxExpr, Math387, Statistics;
procedure Example;
var avec,bvec: Vector;
  hres: THypothesisResult;
  Signif: double;
begin
  avec.Size(1000,false);
  RandomWeibull(2.5,1,avec);
  // filter original data, retain only sorted unique values
  Unique(avec,bvec);
  ShapiroFrancia(bvec,hres,signif);
  // Significance approx. 0
  // hres = hrReject -> data is not coming from normal distribution
end;

#include "MtxExpr.hpp"
#include "Math387.hpp"
#include "Statistics.hpp"
void __fastcall Example()
{
  sVector a,b;
  a.Size(1000,false);
  RandomWeibull(2.5,1.0,a);
  // filter original data, retain only sorted unique values
  Unique(a,b, NULL);
  THypothesisResult hres;
  double sign;
  ShapiroFrancia(b,hres, sign,htTwoTailed,0.05);
  // Significance approx. 0
  // hres = hrReject -> data is not coming from normal distribution
}

Statistics, Functions, Example, See Also

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