std::fisher_f_distribution

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Pseudo-random number generation
 
std::fisher_f_distribution
 
Defined in header <random>
template< class RealType = double >
class fisher_f_distribution;
 (since C++11)

Produces random numbers according to the F-distribution:

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

m and 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

(C++11)
 constructs new distribution
(public member function)
(C++11)
 resets the internal state of the distribution
(public member function)
Generation
(C++11)
 generates the next random number in the distribution
(public member function)
Characteristics
(C++11)
 returns the distribution parameters
(public member function)
(C++11)
 gets or sets the distribution parameter object
(public member function)
(C++11)
 returns the minimum potentially generated value
(public member function)
(C++11)
 returns the maximum potentially generated value
(public member function)

Non-member functions

(C++11)(C++11)(removed in C++20)
 compares two distribution objects
(function)
(C++11)
 performs stream input and output on pseudo-random number distribution
(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.
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