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std::gamma_distribution(3)     C++ Standard Libary    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|I+/-,I^2) =

	e-x/I^2
	I^2I+/-
	A. I(I+/-)

	A. xI+/--1

	where I+/- is known as the shape parameter and I^2 is known as the scale
     parameter. The
	shape parameter is sometimes denoted by the letter k and the scale para-
     meter is
	sometimes denoted by the letter I,.

	For floating-point I+/-, the value obtained is the sum of I+/-	indepen-
     dent exponentially
	distributed random variables, each of which has a mean of I^2.

	std::gamma_distribution satisfies RandomNumberDistribution.

Template parameters
	RealType - The result type generated by the generator. The effect is un-
     defined 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 RandomNumberDis-
     tribution.

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 A Wolfram Web
     Resource.

http://cppreference.com 	   2024.06.10	      std::gamma_distribution(3)
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