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: \(P(x;m,n)=\frac{\Gamma{(\frac{m+n}{2})} }{\Gamma{(\frac{m}{2})}\Gamma{(\frac{n}{2})} }{(\frac{m}{n})}^{\frac{m}{2} }x^{\frac{m}{2}-1}{(1+\frac{m}{n}x)}^{-\frac{m+n}{2} }\)P(x;m,n) =
Γ((m+n)/2) / Γ(m/2) Γ(n/2) (m/n) m/2x (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
|
(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 |
|
| 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
#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
External links
Weisstein, Eric W. "F-Distribution." From MathWorld--A Wolfram Web Resource.
© cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
https://en.cppreference.com/w/cpp/numeric/random/fisher_f_distribution
