#include <GaussDistribution.h>

Public Member Functions
	GaussDistribution (double precision=1e-4)
	GaussDistribution (double mean, double stddev, double precision=1e-4)
bool	isValid ()
double	mean ()
double	part (double a)
	calculate the integral from -inf to a
double	partSigma (double a)
	calculate the integral from -inf to mean+a*stddev
double	prob (double a, double b)
double	rho (double val)
	returns the density of probability for value val
void	setMean (double m)
void	setStddev (double s)
double	stddev ()
	~GaussDistribution ()
Protected Member Functions
double	_calcErrorFunction (double z)
	Calculate the prob integral between -infinity and z by Taylor serie.
Protected Attributes
double	_inv_stddev
double	_mean
double	_precision
	internal precision limit for Taylor serie

Constructor & Destructor Documentation

QGpCoreTools::GaussDistribution::GaussDistribution ( double precision = 1e-4 )

precision is the maximum tolerated difference accepted for probabilities mean and sigma are set to 0

References _inv_stddev, _mean, _precision, and TRACE.

{
  TRACE;
  _precision=precision;
  _mean=0;
  _inv_stddev=0;
}

QGpCoreTools::GaussDistribution::GaussDistribution	(	double	mean,
		double	stddev,
		double	precision = `1e-4`
	)

Initialize the distribution by its basic parameters: mean or x0 stddev or sigma precision is the maximum tolerated difference accepted for probabilities

References _inv_stddev, _mean, _precision, mean(), stddev(), and TRACE.

{
  TRACE;
  _mean=mean;
  _inv_stddev=1.0/stddev;
  _precision=precision;
}

QGpCoreTools::GaussDistribution::~GaussDistribution ( )

References TRACE.

{
  TRACE;
}

Member Function Documentation

double QGpCoreTools::GaussDistribution::_calcErrorFunction ( double z ) [protected]

Calculate the prob integral between -infinity and z by Taylor serie.

References _precision, and TRACE.

{
  TRACE;
  /*
    returns the value of intergral(-inf,z)[exp(-z^2/2)/sqrt(2*pi)]
    =1/2+1/sqrt(2*pi)*Somme(k=0,+inf)[((-1)^k*z^(2*k+1))/((2*k+1)*2^k*k!)]
    we calculate it by recurrence: Somme=Somme[n(k)/(2*k+1)]
    where n(k)=-n(k-1)*z^2/(2*k) with n(0)=z
  */
  if(z<-5) return 0;
  if(z>5) return 1;
  double serie=0,dserie=1e99,n=z;
  int k=0;
  while(dserie>_precision || dserie<-_precision)
    {
      dserie=n/((k << 1)+1);
      serie+=dserie;
      k++;
      n=-n*z*z/(2*k);
    }
  return 0.5+0.398942280402*serie;
}

bool QGpCoreTools::GaussDistribution::isValid ( ) [inline]

{return _inv_stddev!=0;}

double QGpCoreTools::GaussDistribution::mean ( ) [inline]

Referenced by GaussDistribution(), and QGpCoreTools::Random::normal().

{return _mean;}

double QGpCoreTools::GaussDistribution::part ( double a ) [inline]

calculate the integral from -inf to a

Referenced by StatGridAnalyser::on_freqScroll_valueChanged().

                        {
    return _calcErrorFunction((a-_mean)*_inv_stddev);
  }

double QGpCoreTools::GaussDistribution::partSigma ( double a ) [inline]

calculate the integral from -inf to mean+a*stddev

{return _calcErrorFunction(a);}

double QGpCoreTools::GaussDistribution::prob	(	double	a,
		double	b
	)		`[inline]`

Return the probability of interval [a,b] calculate the integral from -inf to a and from -inf to b

                                  {
    return (_calcErrorFunction((b-_mean)*_inv_stddev)
            -_calcErrorFunction((a-_mean)*_inv_stddev));
  }

double QGpCoreTools::GaussDistribution::rho ( double val )

returns the density of probability for value val

References _inv_stddev, _mean, QGpCoreTools::exp(), and TRACE.

Referenced by StatGridAnalyser::on_freqScroll_valueChanged().

{
  TRACE;
  double delta=val-_mean;
  // 1/sqrt(2*M_PI)=0.398942280402
  return 0.398942280402*_inv_stddev*exp(-delta*delta*0.5*_inv_stddev*_inv_stddev);
}