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alpar (Alpar Juttner)
alpar@cs.elte.hu
A better way of generating pareto distr, and swap its parameters. - Pareto distribution is now generated as a composition of a Gamma and an exponential one - Similarly to gamma() and weibull(), the shape parameter became the first one.
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1 file changed with 3 insertions and 7 deletions:
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@@ -753,106 +753,102 @@
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    }
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    /// Gamma distribution with given shape and scale parameter
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    /// This function generates a gamma distribution random number.
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    /// 
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    ///\param k shape parameter (<tt>k>0</tt>)
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    ///\param theta scale parameter
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    ///
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    double gamma(double k,double theta=1.0)
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    {
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      double xi,nu;
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      const double delta = k-std::floor(k);
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      const double v0=M_E/(M_E-delta);
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      do {
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	double V0=1.0-real<double>();
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	double V1=1.0-real<double>();
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	double V2=1.0-real<double>();
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	if(V2<=v0) 
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	  {
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	    xi=std::pow(V1,1.0/delta);
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	    nu=V0*std::pow(xi,delta-1.0);
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	  }
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	else 
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	  {
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	    xi=1.0-std::log(V1);
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	    nu=V0*std::exp(-xi);
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	  }
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      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
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      return theta*(xi-gamma(int(std::floor(k))));
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    }
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    /// Weibull distribution
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    /// This function generates a Weibull distribution random number.
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    /// 
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    ///\param k shape parameter (<tt>k>0</tt>)
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    ///\param lambda scale parameter (<tt>lambda>0</tt>)
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    ///
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    double weibull(double k,double lambda)
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    {
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      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
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    }  
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    /// Pareto distribution
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    /// This function generates a Pareto distribution random number.
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    /// 
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    ///\param k shape parameter (<tt>k>0</tt>)
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    ///\param x_min location parameter (<tt>x_min>0</tt>)
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    ///\param k shape parameter (<tt>k>0</tt>)
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    ///
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    ///\warning This function used inverse transform sampling, therefore may
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    ///suffer from numerical unstability.
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    ///
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    ///\todo Implement a numerically stable method
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    double pareto(double x_min,double k)
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    double pareto(double k,double x_min)
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    {
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      return x_min*pow(1.0-real<double>(),1.0/k);
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      return exponential(gamma(k,1.0/x_min));
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    }  
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    ///@}
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    ///\name Two dimensional distributions
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    ///
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    ///@{
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    /// Uniform distribution on the full unit circle.
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    dim2::Point<double> disc() 
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    {
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      double V1,V2;
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      do {
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	V1=2*real<double>()-1;
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	V2=2*real<double>()-1;
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      } while(V1*V1+V2*V2>=1);
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      return dim2::Point<double>(V1,V2);
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    }
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    /// A kind of two dimensional Gauss distribution
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    /// This function provides a turning symmetric two-dimensional distribution.
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    /// Both coordinates are of standard normal distribution, but they are not
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    /// independent.
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    ///
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    /// \note The coordinates are the two random variables provided by
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    /// the Box-Muller method.
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    dim2::Point<double> gauss2()
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    {
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      double V1,V2,S;
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      do {
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	V1=2*real<double>()-1;
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	V2=2*real<double>()-1;
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	S=V1*V1+V2*V2;
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      } while(S>=1);
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      double W=std::sqrt(-2*std::log(S)/S);
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      return dim2::Point<double>(W*V1,W*V2);
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    }
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    /// A kind of two dimensional exponential distribution
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    /// This function provides a turning symmetric two-dimensional distribution.
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    /// The x-coordinate is of conditionally exponential distribution
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    /// with the condition that x is positive and y=0. If x is negative and 
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    /// y=0 then, -x is of exponential distribution. The same is true for the
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    /// y-coordinate.
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    dim2::Point<double> exponential2() 
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    {
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