std::student_t_distribution
From cppreference.com
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) =
·1 √nπ
· ⎛Γ(
)n+1 2 Γ(
)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.
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 longdouble. |
[edit]Member types
| Member type | Definition |
result_type(C++11) | RealType |
param_type(C++11) | the type of the parameter set, see RandomNumberDistribution. |
[edit]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) |
[edit]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) |
[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, constbool 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;}; constauto[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){constauto q{dv.quot}, r{dv.rem};unsignedchar 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}; constint 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(constauto&[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);constint 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. |
