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) =
   Γ((m+n)/2)
   Γ(m/2) Γ(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 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
   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: '█'
             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 << "┬ " << *max:
                        h ? std::cout << "│ "
                        : std::cout << "┴ " << *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 << "d₁ = " << d1 << ", d₂ = " << d2 << ":\n";
         for (draw_vbars<4, 3>(bars); int n : indices)
             std::cout << std::setw(2) << n << " ";
         std::cout << "\n\n";
     };
     fisher(/* d₁ = */ 1.0f, /* d₂ = */ 5.0f);
     fisher(/* d₁ = */ 15.0f, /* d₂ = */ 10.f);
     fisher(/* d₁ = */ 100.0f, /* d₂ = */ 3.0f);
 }

Possible output:
 d₁ = 1, d₂ = 5:
 ███ ┬ 0.4956
 ███ │
 ███ ▇▇▇ │
 ███ ███ ▇▇▇ ▄▄▄ ▂▂▂ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0021
  0 1 2 3 4 5 6 7 8 9 10 11 12 14
 d₁ = 15, d₂ = 10:
     ███ ┬ 0.6252
     ███ │
     ███ ▂▂▂ │
 ▆▆▆ ███ ███ ▃▃▃ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0023
  0 1 2 3 4 5 6
 d₁ = 100, d₂ = 3:
     ███ ┬ 0.4589
     ███ │
 ▁▁▁ ███ ▅▅▅ │
 ███ ███ ███ ▆▆▆ ▃▃▃ ▂▂▂ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 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 Wolfram Web Resource.