std::fisher_f_distribution - cppreference.com (original) (raw)

std::fisher_f_distribution

| | | | | -------------------------------------------------------------------- | | ------------- | | 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) = (m/n)m/2
x(m/2)-1
(1+)-(m+n)/2

\(\small m\)m and \(\small n\)n are the degrees of freedom.

std::fisher_f_distribution satisfies all requirements of RandomNumberDistribution.

Contents

• 1 Template parameters
• 2 Member types
• 3 Member functions
  • 3.1 Generation
  • 3.2 Characteristics
• 4 Non-member functions
• 5 Example
• 6 External links

[edit] Template parameters

[edit] Member types

[edit] Member functions

[edit] Non-member functions

[edit] Example

#include #include #include #include #include #include #include   template 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 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 bars; std::vector 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