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@@ -758,96 +758,119 @@
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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=E/(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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///
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double pareto(double k,double x_min)
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{
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return exponential(gamma(k,1.0/x_min));
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}
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/// Poisson distribution
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/// This function generates a Poisson distribution random number with
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/// parameter \c lambda.
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///
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/// The probability mass function of this distribusion is
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/// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
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/// \note The algorithm is taken from the book of Donald E. Knuth titled
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/// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
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/// return value.
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int poisson(double lambda)
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{
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const double l = std::exp(-lambda);
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int k=0;
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double p = 1.0;
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do {
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k++;
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p*=real<double>();
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} while (p>=l);
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return k-1;
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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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/// Uniform distribution on the full unit circle.
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///
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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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