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std::fisher_f_distribution

From cppreference.com
< cpp‎ | numeric‎ | random
 
 
 
Pseudo-random number generation
Uniform random bit generators
Engines and engine adaptors
Non-deterministic generator
Distributions
Uniform distributions
Bernoulli distributions
Poisson distributions
Normal distributions
fisher_f_distribution
(C++11)
Sampling distributions
Seed Sequences
(C++11)
C library
 
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.

Contents

[edit] 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.

[edit] Member types

Member type Definition
result_type(C++11) RealType
param_type(C++11) the type of the parameter set, see RandomNumberDistribution.

[edit] Member functions

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

[edit] Non-member functions

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

[edit] Example

#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,
          bool DrawMinMax = true, class Sample>
void draw_vbars(Sample const& s) {
    static_assert((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
    auto cout_n = [](auto const& v, int n) { 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 (float e : s) {
        qr.push_back(std::div(std::lerp(0.f, Height*8, (e - *min)/(*max - *min)), 8));
    }
    for (auto h{Height}; h-- > 0 ;) {
        cout_n(' ', Offset);
        for (auto [q, r] : qr) {
            char d[] = "█"; // == { 0xe2, 0x96, 0x88, 0 }
            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)
            h == Height - 1 ? std::cout << "┬ " << *max:
                     h != 0 ? std::cout << "│"
                            : std::cout << "┴ " << *min;
        cout_n('\n', 1);
    }
}
 
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 (const auto [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";
        draw_vbars<4,3>(bars);
        for (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

[edit] External links

Weisstein, Eric W. "F-Distribution." From MathWorld--A Wolfram Web Resource.