std::student_t_distribution
Defined in header <random> |
||
---|---|---|
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/√nπ · Γ(n+12)n+12Γ(n2)n/2 · ⎛⎜
⎝1+x2/n⎞
⎟
⎠ -n+1/2
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.
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 |
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 n distribution parameter (degrees of freedom) (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()}; 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); } } draw_vbars<8,5>(bars); for (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
External links
Weisstein, Eric W. "Student's t-Distribution." From MathWorld--A Wolfram Web Resource.
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