35 // Generate a floating-point variate conforming to a Beta distribution:
36 //   pdf(x) \propto x^(alpha-1) * (1-x)^(beta-1),
37 // where the params alpha and beta are both strictly positive real values.
40 // to 0 or 1, due to numerical errors when alpha and beta are very different.
42 // Usage note: One usage is that alpha and beta are counts of number of
44 // approximating a beta distribution with a Gaussian distribution with the same
46 // smaller of alpha and beta when the number of trials are sufficiently large,
47 // to quantify how far a beta distribution is from the normal distribution.
57     explicit param_type(result_type alpha, result_type beta)  in param_type()  argument
58         : alpha_(alpha), beta_(beta) {  in param_type()
60       assert(beta >= 0);  in param_type()
62       assert(beta <= (std::numeric_limits<result_type>::max)());  in param_type()
63       if (alpha == 0 || beta == 0) {  in param_type()
65         x_ = (alpha >= beta) ? 1 : 0;  in param_type()
68       // a_ = min(beta, alpha), b_ = max(beta, alpha).  in param_type()
69       if (beta < alpha) {  in param_type()
71         a_ = beta;  in param_type()
76         b_ = beta;  in param_type()
84       // Evaluation of Beta Generation Algorithms, Ying-Chao Hung, et. al.  in param_type()
121     result_type beta() const { return beta_; }  in beta()  function
171       //   Hung et al. Evaluation of beta generation algorithms. Communications
174       //   Zechner, Heinz, and Ernst Stadlober. Generating beta variates via
184     result_type a_;  // the smaller of {alpha, beta}, or 1.0/alpha_ in JOEHNK
185     result_type b_;  // the larger of {alpha, beta}, or 1.0/beta_ in JOEHNK
186     result_type x_;  // alpha + beta, or the result in degenerate cases
188     result_type y_;      // "beta" in Cheng
204   explicit beta_distribution(result_type alpha, result_type beta = 1)
205       : param_(alpha, beta) {}  in param_()  argument
228   result_type beta() const { return param_.beta(); }  in beta()  function
307         // When both alpha and beta are small, x and y are both close to 0, so  in AlgorithmJoehnk()
343   // Based on Cheng, Russell CH. Generating beta variates with nonintegral  in AlgorithmCheng()
402   os << x.alpha() << os.fill() << x.beta();
412   result_type alpha, beta;  variable
417   beta = random_internal::read_floating_point<result_type>(is);
419     x.param(param_type(alpha, beta));