Statistics.cpp

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#include <boost/math/special_functions/fpclassify.hpp>
#include <cmath>

#include "Statistics.hpp"

boost::math::normal MultiplyVarForCoefficient(int coeff, boost::math::normal var)
{
   double mean, st_dev;
   mean = var.mean() * coeff;
   st_dev = var.standard_deviation() * coeff;
   boost::math::normal s(mean, st_dev);
   return s;
}

boost::math::normal VarSum(boost::math::normal x, double c)
{
   boost::math::normal s((x.mean() + c), x.standard_deviation());
   return s;
}

boost::math::normal VarSum(boost::math::normal x, boost::math::normal y)
{
   return VarSum(x, y, 0);
}

boost::math::normal VarSum(boost::math::normal x, boost::math::normal y, double p)
{
   double mean, st_dev;
   mean = x.mean() + y.mean();

   // Mathematically, Cov(X,Y) = p * StandardVariation(x) * StandardVariation(y)
   st_dev = sqrt(pow(x.standard_deviation(), 2) + pow(y.standard_deviation(), 2) +
                 2 * p * x.standard_deviation() * y.standard_deviation());
   boost::math::normal s(mean, st_dev);
   return s;
}

boost::math::lognormal VarSum(std::vector<boost::math::lognormal> v)
{
   if(!v.empty())
   {
      boost::math::lognormal s = v.at(0);
      for(unsigned int i = 1; i < v.size(); i++)
      {
         s = VarSum(s, v.at(i));
      }
      return s;
   }
   return boost::math::lognormal();
}

boost::math::lognormal VarSum(boost::math::lognormal x, boost::math::lognormal y)
{
   return VarSum(x, y, 0);
}

boost::math::lognormal VarSum(boost::math::lognormal s1, boost::math::lognormal s2, double p)
{
   double mean, st_dev;
   double u1, u2;

   u1 = exp(s1.location() + (pow(s1.scale(), 2)) / 2) + exp(s2.location() + (pow(s2.scale(), 2)) / 2);
   u2 = exp(2 * s1.location() + 2 * pow(s1.scale(), 2)) + exp(2 * s2.location() + 2 * pow(s2.scale(), 2)) +
        2 * exp(s1.location() + s2.location()) *
            exp(0.5 * (pow(s1.scale(), 2) + pow(s2.scale(), 2) + 2 * p * s1.scale() * s2.scale()));

   mean = 2 * log(u1) - 0.5 * log(u2);
   st_dev = sqrt(log(u2) - 2 * log(u1));

   boost::math::lognormal s(mean, st_dev);
   return s;
}

boost::math::normal VarMax(boost::math::normal x, boost::math::normal y, double p)
{
   double mean = 0, st_dev = 0, var = 0;
   double a = 0, alpha = 0;

   a = pow((pow(x.standard_deviation(), 2) + pow(y.standard_deviation(), 2) -
            2 * p * x.standard_deviation() * y.standard_deviation()),
           0.5);
   alpha = (x.mean() + y.mean()) / a;

   mean = x.mean() * cdf(x, alpha) + y.mean() * cdf(y, -alpha) + a * pdf(x, alpha);
   var = (pow(x.standard_deviation(), 2) + pow(x.mean(), 2)) * cdf(x, alpha) +
         (pow(y.standard_deviation(), 2) + pow(y.mean(), 2)) * cdf(y, -alpha) +
         (x.mean() + y.mean()) * a * pdf(x, alpha) - pow(mean, 2);

   st_dev = sqrt(var);
   boost::math::normal s(mean, st_dev);
   return s;
}

boost::math::normal VarMax(std::vector<boost::math::normal> v)
{
   if(!v.empty())
   {
      boost::math::normal s = v.at(0);
      for(unsigned int i = 1; i < v.size(); i++)
      {
         s = VarMax(s, v.at(i), 0);
      }
      return s;
   }
   return boost::math::normal();
}

boost::math::normal ComputeStatisticalDelay(double d, int n)
{
   return CreateStatisticalAttribute(d, n);
}

boost::math::lognormal ComputeStatisticalPower(double p, int n)
{
   boost::math::normal s = CreateStatisticalAttribute(p, n);
   boost::math::lognormal v(s.mean(), s.standard_deviation());
   return v;
}

boost::math::normal CreateStatisticalAttribute(double a, int n)
{
   std::vector<int> v;
   v.reserve(static_cast<size_t>(n));
   for(int i = 0; i < n; i++)
   {
      v.push_back(1);
   }

   return CreateStatisticalAttribute(a, v, 0, 1, 1, 0, 1);
}

boost::math::normal CreateStatisticalAttribute(double a, std::vector<int> d, double mean, double st_dev, int d_rand,
                                               double mean_rand, double st_dev_rand)
{
   boost::math::normal ris;
   boost::math::normal x_rand(mean_rand, st_dev_rand);
   ris = MultiplyVarForCoefficient(d_rand, x_rand);

   for(int i : d)
   {
      boost::math::normal temp(mean, st_dev);
      ris = VarSum(ris, MultiplyVarForCoefficient(i, temp));
   }

   return VarSum(ris, a);
}