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CppNormalDistribution

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(C++) Normal distribution

The function GetDensityNormalDistribution returns the density at a certain x of a normal distribution with a certain mean and standard deviation.

The function GetCumulativeDensityNormalDistribution returns the cumulative density at a certain x of a normal distribution with a mean of 0.0 and standard deviation of 0.0. This code was copied from this location.

include <cmath>


double GetDensityNormalDistribution(const double x, const double mean, const double stddev)
{
  const double firstTerm = 1.0 / (stddev * std::sqrt(2.0 * M_PI));
  const double secondTerm = -( (x - mean) * (x - mean) / (2.0 * stddev * stddev) );
  const double result = firstTerm * std::exp(secondTerm);
  return result;
}
double GetCumulativeDensityNormalDistribution(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));
}

How to get a random value from a normal distribution ?

Use the Boost C++ library:

include <boost/random/normal_distribution.hpp>

include <boost/random/lagged_fibonacci.hpp>

include <iostream>

include <vector>


int main()
{
  const double mean = 10.0;
  const double sigma = 1.0;
  boost::normal_distribution<double> norm_dist(mean, sigma);
  boost::lagged_fibonacci19937 engine;
  //Make a histogram
  const int size = static_cast<int>(mean) * 2;
  std::vector<int> histo(size,0);
  for (int i=0; i!=1000000; ++i)
  {
    const double value = norm_dist.operator () <boost::lagged_fibonacci19937>((engine));
    int index = value;
    index = (index < 0 ? 0 : index);
    index = (index > size - 1 ? size - 1 : index);
    ++histo[index];
  }
  //Output histogram
  for (int i=0; i!=size; ++i)
  {
    std::cout << histo[i] << std::endl;
  }
}

or in a function:

include <boost/random/normal_distribution.hpp>

include <boost/random/lagged_fibonacci.hpp>


double normal(const double mean = 0.0, const double sigma = 1.0)
{
  boost::normal_distribution<double> norm_dist(mean, sigma);
  static boost::lagged_fibonacci19937 engine;
  const double value = norm_dist.operator () <boost::lagged_fibonacci19937>((engine));
  return value;
}

Code links

• #include
• cmath (header file)
• const
• double
• exp, std::exp
• include
• return
• std
• std::exp
• std::sqrt
• sqrt

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