std::gamma_distribution(3)

NAME
std::gamma_distribution - std::gamma_distribution

Synopsis
   Defined in header <random>
   template< class RealType = double > (since C++11)
   class gamma_distribution;
   Produces random positive floating-point values x, distributed according to
   probability density function:
   \(\mathsf{p}(x\mid\alpha,\beta) = \frac{e^{-x/\beta}
   }{\beta^\alpha\cdot\Gamma(\alpha)}\cdot x^{\alpha-1} \)P(x|α,β) =
   e-x/β
   βα
   · Γ(α)
   · xα-1
   where α is known as the shape parameter and β is known as the scale parameter. The
   shape parameter is sometimes denoted by the letter k and the scale parameter is
   sometimes denoted by the letter θ.
   For floating-point α, the value obtained is the sum of α independent exponentially
   distributed random variables, each of which has a mean of β.
   std::gamma_distribution satisfies RandomNumberDistribution.

Template parameters
   RealType - The result type generated by the generator. The effect is undefined if
              this is not one of float, double, or long double.

Member types
   Member type Definition
   result_type (C++11) RealType
   param_type (C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions
   constructor constructs new distribution
   (C++11) (public member function)
   reset resets the internal state of the distribution
   (C++11) (public member function)

Generation
   operator() generates the next random number in the distribution
   (C++11) (public member function)

Characteristics
   alpha returns the distribution parameters
   beta (public member function)
   (C++11)
   param gets or sets the distribution parameter object
   (C++11) (public member function)
   min returns the minimum potentially generated value
   (C++11) (public member function)
   max returns the maximum potentially generated value
   (C++11) (public member function)

Non-member functions
   operator==
   operator!= compares two distribution objects
   (C++11) (function)
   (C++11)(removed in C++20)
   operator<< performs stream input and output on pseudo-random number
   operator>> distribution
   (C++11) (function template)

Example
// Run this code
 #include <iomanip>
 #include <iostream>
 #include <map>
 #include <random>
 #include <string>
 int main()
 {
     std::random_device rd;
     std::mt19937 gen(rd());
     // A gamma distribution with alpha = 1, and beta = 2
     // approximates an exponential distribution.
     std::gamma_distribution<> d(1, 2);
     std::map<int, int> hist;
     for (int n = 0; n != 10000; ++n)
         ++hist[2 * d(gen)];
     for (auto const& [x, y] : hist)
         if (y / 100.0 > 0.5)
             std::cout << std::fixed << std::setprecision(1)
                       << x / 2.0 << '-' << (x + 1) / 2.0 << ' '
                       << std::string(y / 100, '*') << '\n';
 }

Possible output:
 0.0-0.5 **********************
 0.5-1.0 ****************
 1.0-1.5 *************
 1.5-2.0 **********
 2.0-2.5 ********
 2.5-3.0 ******
 3.0-3.5 *****
 3.5-4.0 ****
 4.0-4.5 ***
 4.5-5.0 **
 5.0-5.5 **
 5.5-6.0 *
 6.0-6.5 *
 6.5-7.0
 7.0-7.5
 7.5-8.0

External links
   Weisstein, Eric W. "Gamma Distribution." From MathWorld — A Wolfram Web Resource.