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std::fisher_f_distribution

From cppreference.com
< cpp‎ | numeric‎ | random
 
 
Numerics library
 
Pseudo-random number generation
 
 
Defined in header <random>
template< class RealType = double >
class fisher_f_distribution;
(since C++11)

Produces random numbers according to the F-distribution:

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

[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
(C++11)
generates the next random number in the distribution
(public member function) [edit]
Characteristics
(C++11)
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

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

[edit] External links

Weisstein, Eric W. "F-Distribution." From MathWorld — A Wolfram Web Resource.
Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/random/fisher_f_distribution&oldid=160843"

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