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std::extrem...distribution(3)  C++ Standard Libary std::extrem...distribution(3)

NAME
     std::extreme_value_distribution - std::extreme_value_distribution

Synopsis
	Defined in header <random>
	template< class RealType = double >  (since C++11)
	class extreme_value_distribution;

	Produces  random numbers according to the Generalized extreme value dis-
     tribution (it
	is also known as Gumbel Type I, log-Weibull, Fisher-Tippett Type I):

	\({\small  p(x;a,b)  =	\frac{1}{b}   \exp{(\frac{a-x}{b}-\exp{(\frac{a-
     x}{b})})}
	}\)p(x;a,b) =

	1
	b

	expa
	a
	a

	a-x
	b

	- expa
	a
	a

	a-x
	b

	a
	a
	a a
	a
	a

	std::extreme_value_distribution satisfies all requirements of
	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
	a	      returns the distribution parameters
	b	      (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 <algorithm>
      #include <cmath>
      #include <iomanip>
      #include <iostream>
      #include <map>
      #include <random>
      #include <vector>

      template<int  Height  = 5, int BarWidth = 1, int Padding = 1, int Offset =
     0, class Seq>
      void draw_vbars(Seq&& s, const bool DrawMinMax = true)
      {
	  static_assert(0 < Height and 0 < BarWidth and 0 <= Padding  and  0  <=
     Offset);

	  auto cout_n = [](auto&& v, int n = 1)
	  {
	      while (n-- > 0)
		  std::cout << v;
	  };

	  const    auto   [min,   max]	 =   std::minmax_element(std::cbegin(s),
     std::cend(s));

	  std::vector<std::div_t> qr;
	  for (typedef decltype(*std::cbegin(s)) V; V e : s)
	      qr.push_back(std::div(std::lerp(V(0), 8 * Height,
					      (e - *min) / (*max - *min)), 8));

	  for (auto h{Height}; h-- > 0; cout_n('\n'))
	  {
	      cout_n(' ', Offset);

	      for (auto dv : qr)
	      {
		  const auto q{dv.quot}, r{dv.rem};
		  unsigned char d[]{0xe2, 0x96, 0x88, 0}; // Full Block: 'a'
		  q < h ? d[0] = ' ', d[1] = 0 : q == h ? d[2] -= (7 - r) : 0;
		  cout_n(d, BarWidth), cout_n(' ', Padding);
	      }

	      if (DrawMinMax && Height > 1)
		  Height - 1 == h ? std::cout << "a~ " << *max:
				h ? std::cout << "a "
				  : std::cout << "a' " << *min;
	  }
      }

      int main()
      {
	  std::random_device rd{};
	  std::mt19937 gen{rd()};

	  std::extreme_value_distribution<> d{-1.618f, 1.618f};

	  const int norm = 10'000;
	  const float cutoff = 0.000'3f;

	  std::map<int, int> hist{};
	  for (int n = 0; n != norm; ++n)
	      ++hist[std::round(d(gen))];

	  std::vector<float> bars;
	  std::vector<int> indices;
	  for (const auto& [n, p] : hist)
	      if (const float x = p * (1.0f / norm); x > cutoff)
	      {
		  bars.push_back(x);
		  indices.push_back(n);
	      }

	  draw_vbars<8,4>(bars);

	  for (int n : indices)
	      std::cout << ' ' << std::setw(2) << n << "  ";
	  std::cout << '\n';
      }

Possible output:
		     aaaa						    aaaa
     a~ 0.2186
		     aaaa						    aaaa
     a
		aaaa		    aaaa		aaaa		    aaaa
     a
		aaaa		    aaaa		aaaa		    aaaa
     a
		aaaa	       aaaa	      aaaa	     aaaa	    aaaa
     a
		aaaa	    aaaa	aaaa	    aaaa	aaaa	    aaaa
     a
	   aaaa     aaaa     aaaa     aaaa     aaaa	aaaa	  aaaa	    aaaa
     a
      aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa
     aaaa a' 0.0005
       -5    -4   -3   -2   -1	  0    1    2	 3    4    5	6    7	  8    9
     10

External links
	Weisstein, Eric W. "Extreme Value Distribution." From MathWorld a A Wol-
     fram Web
	Resource.

http://cppreference.com 	   2024.06.10	   std::extrem...distribution(3)
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