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std::fisher_f_distribution(3)  C++ Standard Libary std::fisher_f_distribution(3)

NAME
     std::fisher_f_distribution - std::fisher_f_distribution

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

	Produces random numbers according to the F-distribution:

	\(P(x;m,n)=\frac{\Gamma{(\frac{m+n}{2})}
	}{\Gamma{(\frac{m}{2})}\Gamma{(\frac{n}{2})}
     }{(\frac{m}{n})}^{\frac{m}{2}
	}x^{\frac{m}{2}-1}{(1+\frac{m}{n}x)}^{-\frac{m+n}{2} }\)P(x;m,n) =

	I((m+n)/2)
	I(m/2) I(n/2)

	(m/n)m/2
	x(m/2)-1
	(1+

	mx
	n

	)-(m+n)/2

	\(\small m\)m and \(\small n\)n are the degrees of freedom.

	std::fisher_f_distribution  satisfies  all  requirements  of  RandomNum-
     berDistribution.

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
	m	      returns the distribution parameters
	n	      (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()};

	  auto fisher = [&gen](const float d1, const float d2)
	  {
	      std::fisher_f_distribution<float> d{d1 /* m */, d2 /* n */};

	      const int norm = 1'00'00;
	      const float cutoff = 0.002f;

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

	      std::cout << "da = " << d1 << ", da = " << d2 << ":\n";
	      for (draw_vbars<4, 3>(bars); int n : indices)
		  std::cout << std::setw(2) << n << "  ";
	      std::cout << "\n\n";
	  };

	  fisher(/* da = */ 1.0f, /* da = */ 5.0f);
	  fisher(/* da = */ 15.0f, /* da = */ 10.f);
	  fisher(/* da = */ 100.0f, /* da = */ 3.0f);
      }

Possible output:
      da = 1, da = 5:
      aaa						      a~ 0.4956
      aaa						      a
      aaa aaa						      a
      aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa a' 0.0021
       0   1   2   3   4   5   6   7   8   9  10  11  12  14

      da = 15, da = 10:
	  aaa			  a~ 0.6252
	  aaa			  a
	  aaa aaa		  a
      aaa aaa aaa aaa aaa aaa aaa a' 0.0023
       0   1   2   3   4   5   6

      da = 100, da = 3:
	  aaa								      a~
     0.4589
	  aaa								  a
      aaa aaa aaa							  a
      aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa  aaa  aaa  aaa  a'
     0.0021
       0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16

External links
	Weisstein,  Eric W. "F-Distribution." From MathWorld a A Wolfram Web Re-
     source.

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