» Funktionen NORMVERT und NORMINV in c++ sourcecode!

#ifndef NORMINV_H_INCLUDED
#define NORMINV_H_INCLUDED
#include <math.h>

class NormalDistributionConfidenceCalculator
{
public:
    NormalDistributionConfidenceCalculator(void);
    ~NormalDistributionConfidenceCalculator();
    /// <summary>
    ///
    /// </summary>
double InverseNormalDistribution(double probability, double min, double max);
    /// <summary>
    /// Returns the cumulative density function evaluated at A given value.
    /// </summary>
    /// <param name="x">A position on the x-axis.</param>
    /// <param name="mean"></param>
    /// <param name="sigma"></param>
    /// <returns>The cumulative density function evaluated at <C>x</C>.</returns>
    /// <remarks>The value of the cumulative density function at A point <C>x</C> is
    /// probability that the value of A random variable having this normal density is
    /// less than or equal to <C>x</C>.
    /// </remarks>
double NormalDistribution(double x, double mean, double sigma);
    /// <summary>
    /// Given a probability, a mean, and a standard deviation, an x value can be calculated.
    /// </summary>
    /// <returns></returns>
double NormInv(double probability);
    /// <summary>
    ///
    /// </summary>
    /// <param name="probability"></param>
    /// <param name="mean"></param>
    /// <param name="sigma"></param>
    /// <returns></returns>
double NormInv(double probability, double mean, double sigma);
bool AboutEqual(double x, double y);

};
double Epsilon(void);

#endif // NORMINV_H_INCLUDED

#include <iostream>
#include "norminv.h"

NormalDistributionConfidenceCalculator::NormalDistributionConfidenceCalculator(void){};
NormalDistributionConfidenceCalculator::~NormalDistributionConfidenceCalculator(){};

double Epsilon(void)
{
double floatEps = 1;

    while (1 + floatEps / 2 != 1)
        floatEps /= 2;
return floatEps;
}


double NormalDistributionConfidenceCalculator::InverseNormalDistribution(double probability, double minimal, double maximal)
    {
        double x = 0;
        double a = 0;
        double b = 1;

        double precision = pow(10, -3);

        while ((b - a) > precision)
        {
            x = (a + b) / 2;
            if (NormInv(x) > probability)
            {
                b = x;
            }
            else
            {
                a = x;
            }
        }

        if ((maximal > 0) && (minimal > 0))
        {
            x = x * (maximal - minimal) + minimal;
        }
        return x;
    }


double NormalDistributionConfidenceCalculator::NormalDistribution(double x, double mean, double sigma)
    {
        // This algorithm is ported from dcdflib:
        // Cody, W.D. (1993). "ALGORITHM 715: SPECFUN - A Portabel FORTRAN
        // Package of Special Function Routines and Test Drivers"
        // acm Transactions on Mathematical Software. 19, 22-32.
        int i;
        double del, xden, xnum, xsq;
        double result, ccum;
        double arg = (x - mean) / sigma;
        const double sixten = 1.60e0;
        const double sqrpi = 3.9894228040143267794e-1;
        const double thrsh = 0.66291e0;
        const double root32 = 5.656854248e0;
        const double zero = 0.0e0;
        //const double min = double.Epsilon;
        const double minimal = Epsilon();
        double z = arg;
        double y = abs(z);
        const double half = 0.5e0;
        const double one = 1.0e0;

        double a[5] =
            {
                2.2352520354606839287e00, 1.6102823106855587881e02, 1.0676894854603709582e03,
                1.8154981253343561249e04, 6.5682337918207449113e-2
            };

        double b[4] =
            {
                4.7202581904688241870e01, 9.7609855173777669322e02, 1.0260932208618978205e04,
                4.5507789335026729956e04
            };

        double c[9] =
            {
                3.9894151208813466764e-1, 8.8831497943883759412e00, 9.3506656132177855979e01,
                5.9727027639480026226e02, 2.4945375852903726711e03, 6.8481904505362823326e03,
                1.1602651437647350124e04, 9.8427148383839780218e03, 1.0765576773720192317e-8
            };

        double d[8] =
            {
                2.2266688044328115691e01, 2.3538790178262499861e02, 1.5193775994075548050e03,
                6.4855582982667607550e03, 1.8615571640885098091e04, 3.4900952721145977266e04,
                3.8912003286093271411e04, 1.9685429676859990727e04
            };
        double p[6] =
            {
                2.1589853405795699e-1, 1.274011611602473639e-1, 2.2235277870649807e-2,
                1.421619193227893466e-3, 2.9112874951168792e-5, 2.307344176494017303e-2
            };


        double q[5] =
            {
                1.28426009614491121e00, 4.68238212480865118e-1, 6.59881378689285515e-2,
                3.78239633202758244e-3, 7.29751555083966205e-5
            };
        if (y <= thrsh)
        {
            //
            // Evaluate  anorm  for  |X| <= 0.66291
            //
            xsq = zero;
            ///if (y > double.Epsilon) xsq = z * z;
            if (y > Epsilon() ) xsq = z * z;
            xnum = a[4] * xsq;
            xden = xsq;
            for (i = 0; i < 3; i++)
            {
                xnum = (xnum + a[i]) * xsq;
                xden = (xden + b[i]) * xsq;
            }
            result = z * (xnum + a[3]) / (xden + b[3]);
            double temp = result;
            result = half + temp;
        }

        //
        // Evaluate  anorm  for 0.66291 <= |X| <= sqrt(32)
        //
        else if (y <= root32)
        {
            xnum = c[8] * y;
            xden = y;
            for (i = 0; i < 7; i++)
            {
                xnum = (xnum + c[i]) * y;
                xden = (xden + d[i]) * y;
            }
            result = (xnum + c[7]) / (xden + d[7]);
            xsq = floor(y * sixten) / sixten;
            del = (y - xsq) * (y + xsq);
            result = exp(-(xsq * xsq * half)) * exp(-(del * half)) * result;
            ccum = one - result;

            if (z > zero) result = ccum;
        }

            //
        // Evaluate  anorm  for |X| > sqrt(32)
        //
        else
        {
            xsq = one / (z * z);
            xnum = p[5] * xsq;
            xden = xsq;
            for (i = 0; i < 4; i++)
            {
                xnum = (xnum + p[i]) * xsq;
                xden = (xden + q[i]) * xsq;
            }
            result = xsq * (xnum + p[4]) / (xden + q[4]);
            result = (sqrpi - result) / y;
            xsq = floor(z * sixten) / sixten;
            del = (z - xsq) * (z + xsq);
            result = exp(-(xsq * xsq * half)) * exp(-(del * half)) * result;
            ccum = one - result;
            if (z > zero) result = ccum;

        }

        ///if (result < min)
          ///  result = 0.0e0;
          if (result < minimal)
            result = 0.0e0;

        return result;
    }


double NormalDistributionConfidenceCalculator::NormInv(double probability)
    {
        const double a1 = -39.6968302866538;
        const double a2 = 220.946098424521;
        const double a3 = -275.928510446969;
        const double a4 = 138.357751867269;
        const double a5 = -30.6647980661472;
        const double a6 = 2.50662827745924;

        const double b1 = -54.4760987982241;
        const double b2 = 161.585836858041;
        const double b3 = -155.698979859887;
        const double b4 = 66.8013118877197;
        const double b5 = -13.2806815528857;

        const double c1 = -7.78489400243029E-03;
        const double c2 = -0.322396458041136;
        const double c3 = -2.40075827716184;
        const double c4 = -2.54973253934373;
        const double c5 = 4.37466414146497;
        const double c6 = 2.93816398269878;

        const double d1 = 7.78469570904146E-03;
        const double d2 = 0.32246712907004;
        const double d3 = 2.445134137143;
        const double d4 = 3.75440866190742;

        //Define break-points
        // using Epsilon is wrong; see link above for reference to 0.02425 value
        //const double pLow = double.Epsilon;
        const double pLow = 0.02425;

        const double pHigh = 1 - pLow;

        //Define work variables
        double q;
        double result = 0;

        // if argument out of bounds.
        // set it to a value within desired precision.
        if (probability <= 0)
            probability = pLow;

        if (probability >= 1)
            probability = pHigh;

        if (probability < pLow)
        {
            //Rational approximation for lower region
            q = sqrt(-2 * log(probability));
            result = (((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) / ((((d1 * q + d2) * q + d3) * q + d4) * q + 1);
        }
        else if (probability <= pHigh)
        {
            //Rational approximation for lower region
            q = probability - 0.5;
            double r = q * q;
            result = (((((a1 * r + a2) * r + a3) * r + a4) * r + a5) * r + a6) * q /
                     (((((b1 * r + b2) * r + b3) * r + b4) * r + b5) * r + 1);
        }
        else if (probability < 1)
        {
            //Rational approximation for upper region
            q = sqrt(-2 * log(1 - probability));
            result = -(((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) / ((((d1 * q + d2) * q + d3) * q + d4) * q + 1);
        }

        return result;
    }

double NormalDistributionConfidenceCalculator::NormInv(double probability, double mean, double sigma)
    {
        double x = NormInv(probability);
        return sigma * x + mean;
    }

bool AboutEqual(double x, double y) {
    double epsilon = std::max(abs(x), abs(y)) * 1E-15;
    return abs(x - y) <= epsilon;
}

#include <iostream>
#include "norminv.h"


using namespace std;



int main()
{
 NormalDistributionConfidenceCalculator nvt;
 double wert, innen;
 int wouhi = 8;
 double my, x;

 do
 switch(wouhi)
 {
   default:
     cout << "Standardisierte Normalverteilung" << endl;
     cout << "Ende...........................1" << endl;
     cout << "Werte Berechnen................2" << endl;
     cout << "Ihre Wahl: ";
     cin >> wouhi;
     if ((wouhi < 1 ) || (wouhi > 2)) wouhi = 1;
    break;

case 1:
     cout << "Programmende " << endl;
     return EXIT_SUCCESS;
    break;

case 2:
   cout << "My eingeben: ";
   cin >> my;
   cout << " x eingeben: ";
   cin >> x;

   wert = nvt.NormalDistribution(my, x, 1);
   innen = 1 - wert;
   cout.precision(14);
   cout << "Test:" << fixed << wert << "    " << fixed << innen << endl;
   wouhi = 8;

  break;

 }while(wouhi != 1);

 return 0;
}

/******************* Ende des Hauptprogramms ******************/

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