NormalDistribution.h

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#ifndef _utl_NormalDistribution_h_
#define _utl_NormalDistribution_h_


#include <cmath>
#include <utl/Math.h>
#include <utl/MathConstants.h>


namespace utl {

  inline double NormalPDF(const double x)
  { return std::exp(-0.5*Sqr(x)) / kSqrt2Pi; }


  inline double NormalPDF(const double x, const double sigma)
  { return NormalPDF(x / sigma) / sigma; }


  inline double NormalPDF(const double x, const double mean, const double sigma)
  { return NormalPDF(x - mean, sigma); }


  // logarithm-of versions of functions are useful in log-likelihoods
  // where log(Normal) are usually summed up

  inline double LogarithmOfNormalPDF(const double x)
  { return -0.5*Sqr(x) - std::log(kSqrt2Pi); }


  inline double LogarithmOfNormalPDF(const double x, const double sigma)
  { return LogarithmOfNormalPDF(x / sigma) - std::log(sigma); }


  inline double LogarithmOfNormalPDF(const double x, const double mean, const double sigma)
  { return LogarithmOfNormalPDF(x - mean, sigma); }


  inline
  double
  LogarithmOfErfc(const double x)
  {
    if (x < 10)
      return std::log(std::erfc(x));
    // asymptotic expansion
    const double x2 = Sqr(x);
    return -(x2 + std::log(x) + 0.5/x2 + 0.5*std::log(M_PI));
  }


  inline double NormalCDF(const double x)
  { return 0.5 * std::erfc(-x / M_SQRT2); }


  inline double NormalCDF(const double x, const double sigma)
  { return NormalCDF(x / sigma); }


  inline double NormalCDF(const double x, const double mean, const double sigma)
  { return NormalCDF(x - mean, sigma); }


  inline double LogarithmOfNormalComplementCDF(const double x)
  { return -M_LN2 + LogarithmOfErfc(x / M_SQRT2); }


  inline double LogarithmOfNormalComplementCDF(const double x, const double sigma)
  { return LogarithmOfNormalComplementCDF(x / sigma); }


  inline double LogarithmOfNormalComplementCDF(const double x, const double mean, const double sigma)
  { return LogarithmOfNormalComplementCDF(x - mean, sigma); }


  inline double LogarithmOfNormalCDF(const double x)
  { return LogarithmOfNormalComplementCDF(-x); }


  inline double LogarithmOfNormalCDF(const double x, const double sigma)
  { return LogarithmOfNormalCDF(x / sigma); }


  inline double LogarithmOfNormalCDF(const double x, const double mean, const double sigma)
  { return LogarithmOfNormalCDF(x - mean, sigma); }


  double InverseNormalCDF(const double p);


  inline double InverseNormalCDF(const double p, const double sigma)
  { return sigma * InverseNormalCDF(p); }


  inline double InverseNormalCDF(const double p, const double mean, const double sigma)
  { return mean + InverseNormalCDF(p, sigma); }


  double TruncatedNormalPDF(const double x, const double mu, const double sigma,
                            const double xmin, const double xmax);


  // xmax = infinity
  double TruncatedNormalPDF(const double x, const double mu, const double sigma,
                            double xmin);


  inline double PositiveNormalPDF(double x, double mu, double sigma)
  { return TruncatedNormalPDF(x, mu, sigma, 0); }

}


#endif