GetCumulativeDensityNormal is a normal distribution code snippets that calculates the cumulative density at a certain x of a normal distribution with a mean of 0.0 and standard deviation of 1.0.


#include <cmath>



//From http://www.richelbilderbeek.nl/CppGetCumulativeDensityNormal.htm

//Adapted from http://www.ma.ic.ac.uk/~mdavis/course_material/MOP/CumNormDist.txt

double GetCumulativeDensityNormal(const double x)

{

  const double c0 = 0.2316419;

  const double c1 = 1.330274429;

  const double c2 = 1.821255978;

  const double c3 = 1.781477937;

  const double c4 = 0.356563782;

  const double c5 = 0.319381530;

  const double c6 = 0.398942280401;

  const double negative = (x < 0 ? 1.0 : 0.0);

  const double xPos = (x < 0.0 ? -x : x);

  const double k = 1.0 / ( 1.0 + (c0 * xPos));

  const double y1 = (((((((c1*k-c2)*k)+c3)*k)-c4)*k)+c5)*k;

  const double y2 = 1.0 - (c6*std::exp(-0.5*xPos*xPos)*y1);

  return ((1.0-negative)*y2) + (negative*(1.0-y2));

}



//From http://www.richelbilderbeek.nl/CppGetCumulativeDensityNormal.htm

double GetCumulativeDensityNormal(

  const double x,

  const double mean,

  const double stddev)

{

  return GetCumulativeDensityNormal(

    (x - mean) / stddev);

}

GetCumulativeDensityNormal test


#include <cmath>



//From http://www.richelbilderbeek.nl/CppGetCumulativeDensityNormal.htm

//Adapted from http://www.ma.ic.ac.uk/~mdavis/course_material/MOP/CumNormDist.txt

double GetCumulativeDensityNormal(const double x)

{

  const double c0 = 0.2316419;

  const double c1 = 1.330274429;

  const double c2 = 1.821255978;

  const double c3 = 1.781477937;

  const double c4 = 0.356563782;

  const double c5 = 0.319381530;

  const double c6 = 0.398942280401;

  const double negative = (x < 0 ? 1.0 : 0.0);

  const double xPos = (x < 0.0 ? -x : x);

  const double k = 1.0 / ( 1.0 + (c0 * xPos));

  const double y1 = (((((((c1*k-c2)*k)+c3)*k)-c4)*k)+c5)*k;

  const double y2 = 1.0 - (c6*std::exp(-0.5*xPos*xPos)*y1);

  return ((1.0-negative)*y2) + (negative*(1.0-y2));

}



//From http://www.richelbilderbeek.nl/CppGetCumulativeDensityNormal.htm

double GetCumulativeDensityNormal(

  const double x,

  const double mean,

  const double stddev)

{

  return GetCumulativeDensityNormal(

    (x - mean) / stddev);

}



#include <iostream>



int main()

{

  std::cout

  << "\nx: -4.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-4.0)

  << "\nx: -3.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-3.0)

  << "\nx: -2.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-2.0)

  << "\nx: -1.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-1.0)

  << "\nx:  0.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 0.0)

  << "\nx:  1.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 1.0)

  << "\nx:  2.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 2.0)

  << "\nx:  3.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 3.0)

  << "\nx:  4.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 4.0)

  << "\n"

  << "\nx: -4.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-4.0,0.0,1.0)

  << "\nx: -3.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-3.0,0.0,1.0)

  << "\nx: -2.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-2.0,0.0,1.0)

  << "\nx: -1.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-1.0,0.0,1.0)

  << "\nx:  0.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 0.0,0.0,1.0)

  << "\nx:  1.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 1.0,0.0,1.0)

  << "\nx:  2.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 2.0,0.0,1.0)

  << "\nx:  3.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 3.0,0.0,1.0)

  << "\nx:  4.0, mean: 0.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 4.0,0.0,1.0)

  << "\n"

  << "\nx: -4.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal(-4.0,0.0,2.0)

  << "\nx: -3.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal(-3.0,0.0,2.0)

  << "\nx: -2.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal(-2.0,0.0,2.0)

  << "\nx: -1.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal(-1.0,0.0,2.0)

  << "\nx:  0.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal( 0.0,0.0,2.0)

  << "\nx:  1.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal( 1.0,0.0,2.0)

  << "\nx:  2.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal( 2.0,0.0,2.0)

  << "\nx:  3.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal( 3.0,0.0,2.0)

  << "\nx:  4.0, mean: 0.0, stdDev: 2.0, CDN: "

  << GetCumulativeDensityNormal( 4.0,0.0,2.0)

  << "\n"

  << "\nx: -4.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-4.0,1.0,1.0)

  << "\nx: -3.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-3.0,1.0,1.0)

  << "\nx: -2.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-2.0,1.0,1.0)

  << "\nx: -1.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal(-1.0,1.0,1.0)

  << "\nx:  0.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 0.0,1.0,1.0)

  << "\nx:  1.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 1.0,1.0,1.0)

  << "\nx:  2.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 2.0,1.0,1.0)

  << "\nx:  3.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 3.0,1.0,1.0)

  << "\nx:  4.0, mean: 1.0, stdDev: 1.0, CDN: "

  << GetCumulativeDensityNormal( 4.0,1.0,1.0);

}

Screen output:


Starting /MyFolder/MyProject...



x: -4.0, mean: 0.0, stdDev: 1.0, CDN: 3.1686e-05

x: -3.0, mean: 0.0, stdDev: 1.0, CDN: 0.00134997

x: -2.0, mean: 0.0, stdDev: 1.0, CDN: 0.0227501

x: -1.0, mean: 0.0, stdDev: 1.0, CDN: 0.158655

x: 0.0, mean: 0.0, stdDev: 1.0, CDN: 0.5

x: 1.0, mean: 0.0, stdDev: 1.0, CDN: 0.841345

x: 2.0, mean: 0.0, stdDev: 1.0, CDN: 0.97725

x: 3.0, mean: 0.0, stdDev: 1.0, CDN: 0.99865

x: 4.0, mean: 0.0, stdDev: 1.0, CDN: 0.999968



x: -4.0, mean: 0.0, stdDev: 1.0, CDN: 3.1686e-05

x: -3.0, mean: 0.0, stdDev: 1.0, CDN: 0.00134997

x: -2.0, mean: 0.0, stdDev: 1.0, CDN: 0.0227501

x: -1.0, mean: 0.0, stdDev: 1.0, CDN: 0.158655

x: 0.0, mean: 0.0, stdDev: 1.0, CDN: 0.5

x: 1.0, mean: 0.0, stdDev: 1.0, CDN: 0.841345

x: 2.0, mean: 0.0, stdDev: 1.0, CDN: 0.97725

x: 3.0, mean: 0.0, stdDev: 1.0, CDN: 0.99865

x: 4.0, mean: 0.0, stdDev: 1.0, CDN: 0.999968



x: -4.0, mean: 0.0, stdDev: 2.0, CDN: 0.0227501

x: -3.0, mean: 0.0, stdDev: 2.0, CDN: 0.0668072

x: -2.0, mean: 0.0, stdDev: 2.0, CDN: 0.158655

x: -1.0, mean: 0.0, stdDev: 2.0, CDN: 0.308538

x: 0.0, mean: 0.0, stdDev: 2.0, CDN: 0.5

x: 1.0, mean: 0.0, stdDev: 2.0, CDN: 0.691462

x: 2.0, mean: 0.0, stdDev: 2.0, CDN: 0.841345

x: 3.0, mean: 0.0, stdDev: 2.0, CDN: 0.933193

x: 4.0, mean: 0.0, stdDev: 2.0, CDN: 0.97725



x: -4.0, mean: 1.0, stdDev: 1.0, CDN: 2.87105e-07

x: -3.0, mean: 1.0, stdDev: 1.0, CDN: 3.1686e-05

x: -2.0, mean: 1.0, stdDev: 1.0, CDN: 0.00134997

x: -1.0, mean: 1.0, stdDev: 1.0, CDN: 0.0227501

x: 0.0, mean: 1.0, stdDev: 1.0, CDN: 0.158655

x: 1.0, mean: 1.0, stdDev: 1.0, CDN: 0.5

x: 2.0, mean: 1.0, stdDev: 1.0, CDN: 0.841345

x: 3.0, mean: 1.0, stdDev: 1.0, CDN: 0.97725

x: 4.0, mean: 1.0, stdDev: 1.0, CDN: 0.99865

/MyFolder/MyProject exited with code 0

Original code

GetCumulativeDensityNormal is adapted from the code snippet below:


//Original code from http://www.ma.ic.ac.uk/~mdavis/course_material/MOP/CumNormDist.txt

double N(double x)

{

  int neg = (x<0);

  if(neg) x *= -1;

  double k(1/(1+0.2316419*x));

  double y=((((1.330274429*k-1.821255978)*k+1.781477937)*k-0.356563782)*k+0.319381530)*k;

  y = 1.0 - 0.398942280401*exp(-0.5*x*x)*y;

  return (1-neg)*y + neg*(1-y);

}

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(C++) GetCumulativeDensityNormal

GetCumulativeDensityNormal test

Original code