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

std::student_t_distribution

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

Produces random floating-point values x, distributed according to probability density function:

\(p(x|n) = \frac{1}{\sqrt{n\pi} } \cdot \frac{\Gamma(\frac{n+1}{2})}{\Gamma(\frac{n}{2})} \cdot (1+\frac{x^2}{n})^{-\frac{n+1}{2} } \)p(x|n) = · · ⎛
⎜
⎝1+⎞
⎟
⎠ -

where n is known as the number of degrees of freedom. This distribution is used when estimating the mean of an unknown normally distributed value given n + 1 independent measurements, each with additive errors of unknown standard deviation, as in physical measurements. Or, alternatively, when estimating the unknown mean of a normal distribution with unknown standard deviation, given n + 1 samples.

std::student_t_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()};   std::student_t_distribution<> d{10.0f};   const int norm = 10'000; const float cutoff = 0.000'3f;   std::map<int, int> hist{}; for (int n = 0; n != norm; ++n) ++hist[std::round(d(gen))];   std::vector bars; std::vector indices; for (const auto& [n, p] : hist) if (float x = p * (1.0f / norm); cutoff < x) { bars.push_back(x); indices.push_back(n); }   for (draw_vbars<8, 5>(bars); const int n : indices) std::cout << " " << std::setw(2) << n << " "; std::cout << '\n'; }

Possible output:

                    █████                               ┬ 0.3753
                    █████                               │
              ▁▁▁▁▁ █████                               │
              █████ █████ ▆▆▆▆▆                         │
              █████ █████ █████                         │
              █████ █████ █████                         │
        ▄▄▄▄▄ █████ █████ █████ ▄▄▄▄▄                   │

▁▁▁▁▁ ▃▃▃▃▃ █████ █████ █████ █████ █████ ▃▃▃▃▃ ▁▁▁▁▁ ▁▁▁▁▁ ┴ 0.0049 -4 -3 -2 -1 0 1 2 3 4 5

[edit] External links