Computation of the bivariate Statistics of two Variables. More...

#include <STK_Stat_BivariateRealReal.h>

Collaboration diagram for STK::Stat::Bivariate< Real, Real, TContainer1D >:

Public Member Functions
	Bivariate (ITContainer1D< Real, TContainer1D > const &X, ITContainer1D< Real, TContainer1D > const &Y)
	Default constructor.
	Bivariate (ITContainer1D< Real, TContainer1D > const &X, ITContainer1D< Real, TContainer1D > const &Y, TContainer1D const &W)
	Default constructor.
	Bivariate (Bivariate< Real, Real, TContainer1D > const &stat)
	Copy constructor.
virtual	~Bivariate ()
	virtual destructor.
Bivariate &	operator= (Bivariate< Real, Real, TContainer1D > const &stat)
	Operator = : overwrite the BivariateRealReal with stat.
void	setData (ITContainer1D< Real, TContainer1D > const &X, ITContainer1D< Real, TContainer1D > const &Y)
	set a new data sets
void	setData (ITContainer1D< Real, TContainer1D > const &X, ITContainer1D< Real, TContainer1D > const &Y, TContainer1D const &W)
	set a new data sets
Univariate< Real, TContainer1D > const &	xStat () const
	get statistics of the first variable
Univariate< Real, TContainer1D > const &	yStat () const
	get statistics of the first variable
Real const &	covariance () const
	get covariance between the variables
Real const &	correlation () const
	get correlation between the variables
Real const &	unbiasedCovariance () const
	get the unbiased covariance between the variables
Real const &	unbiasedCorrelation () const
	get the unbiased correlation between the variables
Protected Member Functions
void	compCovariance ()
	compute the covariance
void	compWeightedCovariance ()
	compute the weighted covariance
Protected Attributes
TContainer1D	X_
	reference on the X data set.
TContainer1D	Y_
	reference on the Y data set.
TContainer1D	W_
	local copy of the weights
Univariate< Real, TContainer1D >	xStat_
	Statistics of the X variable.
Univariate< Real, TContainer1D >	yStat_
	Statistics of the Y variable.
Real	cov_
	covariance between X and Y
Real	ucov_
	unbiased covariance between X and Y
Real	cor_
	correlation between X and Y
Real	ucor_
	unbiased correlation between X and Y
Real	sumWeights_
	Sum of the weights.
Real	sum2Weights_
	Sum of the square of the weights.

Detailed Description

template<class TContainer1D>
class STK::Stat::Bivariate< Real, Real, TContainer1D >

Computation of the bivariate Statistics of two Variables.

The template parameter TContainer1D is the type of container used for storing the data : It should derive from ITContainer1D and contain elements of type Real.

This specialized class compute the Real univariate descriptive statistics of X and Y and the covariance between X and Y.

The covariance between X and Y will be computed using the formula

See also:: Mark Galassi, Jim Davies, James Theiler, Brian Gough, Gerard Jungman, Michael Booth, and Fabrice Rossi. http://www.gnu.org/software/gsl/manual GNU Scientific Library - Reference manual, Version 1.15, 2011. http://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html Sec. 21.7 Weighted Samples

$cov(X,Y)=\frac{\sum_{i=1}^{N}w_i}{\left(\sum_{i=1}^{N}w_i\right)^2-\sum_{i=1}^{N}w_i^2} \sum_{i=1}^N w_i \left( x_{i}-\bar{x} \right) \left( y_{i}-\bar{y} \right).$

Definition at line 68 of file STK_Stat_BivariateRealReal.h.

Constructor & Destructor Documentation

template<class TContainer1D >

STK::Stat::Bivariate< Real, Real, TContainer1D >::Bivariate	(	ITContainer1D< Real, TContainer1D > const &	X,
		ITContainer1D< Real, TContainer1D > const &	Y
	)		`[inline]`

Default constructor.

Copy locally the vectors X and Y and compute the univariate and bivariate statistics.

Parameters:

X	the first variable
Y	the second variable

Definition at line 76 of file STK_Stat_BivariateRealReal.h.

             : X_(X.asLeaf())
             , Y_(Y.asLeaf())
             , W_()
             , xStat_(X)
             , yStat_(Y)
             , cov_(0.)
             , ucov_(0.)
             , cor_(0.)
             , ucor_(0.)
             , sumWeights_(0.0)
             , sum2Weights_(0.0)
    {
      compCovariance();
    }

template<class TContainer1D >

STK::Stat::Bivariate< Real, Real, TContainer1D >::Bivariate	(	ITContainer1D< Real, TContainer1D > const &	X,
		ITContainer1D< Real, TContainer1D > const &	Y,
		TContainer1D const &	W
	)		`[inline]`

Default constructor.

Compute the univariate statistics of the two variables. The

Parameters:

X	the first variable
Y	the second variable
W	the weights

Definition at line 100 of file STK_Stat_BivariateRealReal.h.

             : X_(X.asLeaf())
             , Y_(Y.asLeaf())
             , W_(W)
             , xStat_(X, W)
             , yStat_(Y, W)
             , cov_(0.)
             , ucov_(0.)
             , cor_(0.)
             , ucor_(0.)
             , sumWeights_(0.0)
             , sum2Weights_(0.0)
    {
      compWeightedCovariance();
    }

template<class TContainer1D >

STK::Stat::Bivariate< Real, Real, TContainer1D >::Bivariate ( Bivariate< Real, Real, TContainer1D > const & stat ) [inline]

Copy constructor.

Parameters:

stat	the statistics to copy

Definition at line 121 of file STK_Stat_BivariateRealReal.h.

              : xStat_(stat.xStat_)
              , yStat_(stat.yStat_)
              , cov_(stat.cov_)
              , ucov_(stat.ucov_)
              , cor_(stat.cor_)
              , ucor_(stat.ucor_)
              , sumWeights_(stat.nweight_)
              , sum2Weights_(stat.nweight2_)
    { }

template<class TContainer1D >

virtual STK::Stat::Bivariate< Real, Real, TContainer1D >::~Bivariate ( ) [inline, virtual]

virtual destructor.

Definition at line 133 of file STK_Stat_BivariateRealReal.h.

{ ;}

Member Function Documentation

template<class TContainer1D >

Bivariate& STK::Stat::Bivariate< Real, Real, TContainer1D >::operator= ( Bivariate< Real, Real, TContainer1D > const & stat ) [inline]

Operator = : overwrite the BivariateRealReal with stat.

Parameters:

stat	the statistics to copy

Returns:: this object

Definition at line 139 of file STK_Stat_BivariateRealReal.h.

References cor_, cov_, ucor_, ucov_, W_, xStat_, STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::xStat_, yStat_, and STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::yStat_.

    {
      xStat_ = stat.xStat_;
      yStat_ = stat.yStat_;
      W_     = stat.W_;
      cov_   = stat.cov_;
      ucov_  = stat.ucov_;
      cor_   = stat.cor_;
      ucor_  = stat.ucor_;
      return *this;
    }

template<class TContainer1D >

void STK::Stat::Bivariate< Real, Real, TContainer1D >::setData	(	ITContainer1D< Real, TContainer1D > const &	X,
		ITContainer1D< Real, TContainer1D > const &	Y
	)		`[inline]`

set a new data sets

Parameters:

X	the first variable
Y	the second variable

Definition at line 155 of file STK_Stat_BivariateRealReal.h.

References STK::IRecursiveTemplate< TContainer1D >::asLeaf(), STK::Stat::Univariate< TYPE, TContainer1D >::setData(), STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::xStat_, and STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::yStat_.

    {
      X_ = X.asLeaf();
      Y_ = Y.asLeaf();
      W_.clear();
      xStat_.setData(X);
      yStat_.setData(Y);
      compCovariance();
    }

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template<class TContainer1D >

void STK::Stat::Bivariate< Real, Real, TContainer1D >::setData	(	ITContainer1D< Real, TContainer1D > const &	X,
		ITContainer1D< Real, TContainer1D > const &	Y,
		TContainer1D const &	W
	)		`[inline]`

set a new data sets

Parameters:

X	the first variable
Y	the second variable
W	the weights to apply

Definition at line 172 of file STK_Stat_BivariateRealReal.h.

References STK::IRecursiveTemplate< TContainer1D >::asLeaf(), STK::Stat::Univariate< TYPE, TContainer1D >::setData(), STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::xStat_, and STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::yStat_.

    {
      X_ = X.asLeaf();
      Y_ = Y.asLeaf();
      W_ = W;
      xStat_.setData(X, W);
      yStat_.setData(Y, W);
      compWeightedCovariance();
    }

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template<class TContainer1D >

Univariate<Real, TContainer1D> const& STK::Stat::Bivariate< Real, Real, TContainer1D >::xStat ( ) const [inline]

get statistics of the first variable

Returns:: the statistics of X

Definition at line 188 of file STK_Stat_BivariateRealReal.h.

References STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::xStat_.

{return xStat_;}

template<class TContainer1D >

Univariate<Real, TContainer1D> const& STK::Stat::Bivariate< Real, Real, TContainer1D >::yStat ( ) const [inline]

get statistics of the first variable

Returns:: the statistics of Y

Definition at line 192 of file STK_Stat_BivariateRealReal.h.

References STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::yStat_.

{return yStat_;}

template<class TContainer1D >

Real const& STK::Stat::Bivariate< Real, Real, TContainer1D >::covariance ( ) const [inline]

get covariance between the variables

Returns:: the covariance between X and Y

Definition at line 196 of file STK_Stat_BivariateRealReal.h.

{ return cov_;}

template<class TContainer1D >

Real const& STK::Stat::Bivariate< Real, Real, TContainer1D >::correlation ( ) const [inline]

get correlation between the variables

Returns:: the correlation between X and Y

Definition at line 200 of file STK_Stat_BivariateRealReal.h.

{ return cor_;}

template<class TContainer1D >

Real const& STK::Stat::Bivariate< Real, Real, TContainer1D >::unbiasedCovariance ( ) const [inline]

get the unbiased covariance between the variables

Returns:: the unbiased covariance between X and Y

Definition at line 204 of file STK_Stat_BivariateRealReal.h.

{ return ucov_;}

template<class TContainer1D >

Real const& STK::Stat::Bivariate< Real, Real, TContainer1D >::unbiasedCorrelation ( ) const [inline]

get the unbiased correlation between the variables

Returns:: the unbiased correlation between X and Y

Definition at line 208 of file STK_Stat_BivariateRealReal.h.

{ return ucor_;}

template<class TContainer1D >

void STK::Stat::Bivariate< Real, Real, TContainer1D >::compCovariance ( ) [inline, protected]

compute the covariance

Definition at line 235 of file STK_Stat_BivariateRealReal.h.

References STK::Range::first(), STK::Range::inf(), STK::Range::last(), STK::Range::size(), STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::xStat_, and STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::yStat_.

    {
      // get dimensions
      Range com = STK::Range::inf(X_.range(),Y_.range());
      const Integer first = com.first(), last = com.last();
      Integer nobs = com.size();
      // get means
      Real xMean = xStat_.mean(), yMean= yStat_.mean();
      // compute covariance
      Real xsum  = 0.0, ysum = 0.0, xdev, ydev;
      cov_ = 0.;
      for (Integer i=first; i<=last; i++)
      {
        if (Arithmetic<Real>::isFinite(X_[i]) && Arithmetic<Real>::isFinite(Y_[i]))
        {
          xsum += (xdev = X_[i] - xMean); // deviation from the mean
          ysum += (ydev = Y_[i] - yMean); // deviation from the mean
          cov_ += (xdev*ydev);         // squared value
        }
        else nobs--;
      }
      if (nobs > 1)
      {
        ucov_ = (cov_ - (xsum*ysum)/(Real)nobs)/(Real)(nobs -1);
        ucor_ = ucov_/(xStat_.unbiasedStd()*yStat_.unbiasedStd());
        cov_  = (cov_ - (xsum*ysum)/(Real)nobs)/(Real)(nobs);
        cor_  = cov_/(xStat_.std()*yStat_.std());
      }
      else
      {
        if (nobs == 1)
        {
          cov_ = 0.;
          cor_ = 0.;
          ucov_ = Arithmetic<Real>::NA();
          ucor_ = Arithmetic<Real>::NA();
        }
        // no observations
        cov_ = Arithmetic<Real>::NA();
        cor_ = Arithmetic<Real>::NA();
        ucov_ = Arithmetic<Real>::NA();
        ucor_ = Arithmetic<Real>::NA();
      }
    }

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template<class TContainer1D >

void STK::Stat::Bivariate< Real, Real, TContainer1D >::compWeightedCovariance ( ) [inline, protected]

compute the weighted covariance

Definition at line 281 of file STK_Stat_BivariateRealReal.h.

References STK::abs(), STK::Range::first(), STK::Range::inf(), STK::Range::last(), STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::xStat_, and STK::Stat::Bivariate< XTYPE, YTYPE, TContainer1D >::yStat_.

    {
      // get dimensions
      Range com = STK::Range::inf(X_.range(),Y_.range());
      Integer first = com.first(), last = com.last();
      // get means
      Real xMean = xStat_.mean(), yMean= yStat_.mean();
      // compute covariance
      Real xsum  = 0.0, ysum = 0.0, xdev, ydev;
      sumWeights_ = 0.0;
      sum2Weights_ = 0.0;
      // sum
      cov_ = 0.0;
      for (Integer i=first; i<=last; i++)
      {
        if (Arithmetic<Real>::isFinite(X_[i]) && Arithmetic<Real>::isFinite(Y_[i]))
        {
          xsum += (xdev = X_[i] - xMean); // deviation from the mean
          ysum += (ydev = Y_[i] - yMean); // deviation from the mean
          Real Wi = abs((Real)W_[i]);
          cov_ += Wi * (xdev*ydev);         // cross product
          sumWeights_  += Wi;           // sum absolute weights
          sum2Weights_ += Wi * Wi;     // sum squared weights
       }
     }
     // not pathological weights
     if (sumWeights_*sumWeights_ > sum2Weights_)
     {
       ucov_ = (cov_ - xsum*ysum/sumWeights_)/(sumWeights_ - sum2Weights_/sumWeights_);
       ucor_ = ucov_/(xStat_.unbiasedStd()*yStat_.unbiasedStd());
       cov_ = (cov_ - xsum*ysum)/(sumWeights_);
       cor_ = cov_/(xStat_.std()*yStat_.std());
     }
     else
     {
       if (sumWeights_) // if sum of the weights is not 0
       {
         cov_ = 0.;
         cor_ = 0.;
         ucov_ = Arithmetic<Real>::NA();
         ucor_ = Arithmetic<Real>::NA();
       }
       // no weigths
       cov_ = Arithmetic<Real>::NA();
       cor_ = Arithmetic<Real>::NA();
       ucov_ = Arithmetic<Real>::NA();
       ucor_ = Arithmetic<Real>::NA();
     }
   }