{Statistical procedures 
author: Nikolai V. Shokhirev  
created: 2002.02.02
last modified: 2003.07.07
ŠNikolai V. Shokhirev, 2002-2003 }
unit uStatUtils;

interface

uses
  uMatTypes, uDynArrays, {uComplexType,} uDynData;

{ average = sum(x[i])/n
  variance = m2 = sum((x[i]-average)**2)/n
  deviation = sqrt(m2) - standard deviation
  skewness = m3/(m2*sqrt(m2));
  kurtosis = m4/sqr(m2);
}procedure StatMoments(const x: IFArr1D; var average, variance, deviation,
                                                    skewness, kurtosis: TFloat);

procedure StatMoments0(const x: IFArr1D; var average, variance, deviation,
                                                    skewness, kurtosis: TFloat);

{
  xav1 = sum(x1[i])/n
  xav2 = sum(x2[i])/n
  var1 = sum((x1[i]-xav1)**2)/n
  var2 = sum((x2[i]-xav2)**2)/n
  cov - covariance = sum((x1[i]-xav1)*(x2[i]-xav2))/n
  corr := cov/sqrt(var1*var2);
}
procedure covariance(const x1x2: IFData1D;
                                 var x1av, x2av, var1, var2, cov, corr: TFloat);

implementation

end.

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