std::student_t_distribution
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student_t_distribution
(C++11)
(C++11)
(C++11)
(C++11)
std::student_t_distribution
Member functions
Generation
Characteristics
Non-member functions
(C++11)(C++11)(until C++20)
(C++11)(C++11)
Defined in header
<random>
template< class RealType = double >
class student_t_distribution;
(since C++11)
class student_t_distribution;
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√nπ·Γ(n+12)Γ(· ⎛n2)
⎜
⎝1+x2n⎞
⎟
⎠ -n+12
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
[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
[edit] Member functions
Generation
Characteristics
[edit] Non-member functions
(C++11)
(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()}; 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 <float> bars; std::vector <int> 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
Weisstein, Eric W. "Student's t-Distribution." From MathWorld — A Wolfram Web Resource.