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

std::chi_squared_distribution

| | | | | ----------------------------------------------------------------------- | | ------------- | | template< class RealType = double > class chi_squared_distribution; | | (since C++11) |

The chi_squared_distribution produces random numbers \(\small x>0\)x>0 according to the Chi-squared distribution:

\({\small f(x;n) = }\frac{x^{(n/2)-1}\exp{(-x/2)} }{\Gamma{(n/2)}2^{n/2} }\)f(x;n) =

\(\small\Gamma\)Γ is the Gamma function (See also std::tgamma) and \(\small n\)n are the degrees of freedom (default 1).

std::chi_squared_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 χ2 = [&gen](const float dof) { std::chi_squared_distribution d{dof / 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 << "dof = " << dof << ":\n";   for (draw_vbars<4, 3>(bars); int n : indices) std::cout << std::setw(2) << n << " "; std::cout << "\n\n"; };   for (float dof : {1.f, 2.f, 3.f, 4.f, 6.f, 9.f}) χ2(dof); }

Possible output:

dof = 1: ███ ┬ 0.5271 ███ │ ███ ███ │ ███ ███ ▇▇▇ ▃▃▃ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.003 0 1 2 3 4 5 6 7 8   dof = 2: ███ ┬ 0.3169 ▆▆▆ ███ ▃▃▃ │ ███ ███ ███ ▄▄▄ │ ███ ███ ███ ███ ▇▇▇ ▄▄▄ ▃▃▃ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.004 0 1 2 3 4 5 6 7 8 9 10   dof = 3: ███ ▃▃▃ ┬ 0.2439 ███ ███ ▄▄▄ │ ▃▃▃ ███ ███ ███ ▇▇▇ ▁▁▁ │ ███ ███ ███ ███ ███ ███ ▆▆▆ ▄▄▄ ▃▃▃ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0033 0 1 2 3 4 5 6 7 8 9 10 11 12   dof = 4: ▂▂▂ ███ ▃▃▃ ┬ 0.1864 ███ ███ ███ ███ ▂▂▂ │ ███ ███ ███ ███ ███ ▅▅▅ ▁▁▁ │ ▅▅▅ ███ ███ ███ ███ ███ ███ ███ ▆▆▆ ▄▄▄ ▃▃▃ ▂▂▂ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0026 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   dof = 6: ▅▅▅ ▇▇▇ ███ ▂▂▂ ┬ 0.1351 ▅▅▅ ███ ███ ███ ███ ▇▇▇ ▁▁▁ │ ▁▁▁ ███ ███ ███ ███ ███ ███ ███ ▅▅▅ ▂▂▂ │ ▁▁▁ ███ ███ ███ ███ ███ ███ ███ ███ ███ ███ ███ ▅▅▅ ▄▄▄ ▃▃▃ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0031 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18   dof = 9: ▅▅▅ ▇▇▇ ███ ███ ▄▄▄ ▂▂▂ ┬ 0.1044 ▃▃▃ ███ ███ ███ ███ ███ ███ ▅▅▅ ▁▁▁ │ ▄▄▄ ███ ███ ███ ███ ███ ███ ███ ███ ███ ▆▆▆ ▃▃▃ │ ▄▄▄ ███ ███ ███ ███ ███ ███ ███ ███ ███ ███ ███ ███ ███ ▆▆▆ ▄▄▄ ▃▃▃ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0034 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

[edit] External links