std::chi_squared_distribution
From cppreference.com
Defined in header <random> | ||
template<class RealType =double> class chi_squared_distribution; | (since C++11) | |
The chi_squared_distribution produces random numbers x>0 according to the Chi-squared distribution:
- f(x;n) =
x(n/2)-1
e-x/2Γ(n/2) 2n/2
Γ is the Gamma function (See also std::tgamma) and n are the degrees of freedom (default 1).
std::chi_squared_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 | |
(C++11) | returns the degrees of freedom (n) distribution parameter (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()}; auto χ2=[&gen](constfloat dof){ std::chi_squared_distribution<float> d{dof /* n */}; constint norm =1'00'00;constfloat cutoff =0.002f; 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(autoconst&[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
| 1. | Weisstein, Eric W. "Chi-Squared Distribution." From MathWorld — A Wolfram Web Resource. |
| 2. | Chi-squared distribution — From Wikipedia. |
