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(C++11)(C++11)(until C++20) | ||||
(C++11)(C++11) |
Defined in header <random> | ||
template<class RealType=double> class chi_squared_distribution; | (since C++11) | |
Thechi_squared_distribution produces random numbers\(\small x>0\)x>0 according to theChi-squared distribution:
| x(n/2)-1 e-x/2 |
| Γ(n/2) 2n/2 |
\(\small\Gamma\)Γ is theGamma function (See alsostd::tgamma) and\(\small n\)n are thedegrees of freedom (default 1).
std::chi_squared_distribution satisfies all requirements ofRandomNumberDistribution.
Contents |
| RealType | - | The result type generated by the generator. The effect is undefined if this is not one offloat,double, orlongdouble. |
| Member type | Definition |
result_type(C++11) | RealType |
param_type(C++11) | the type of the parameter set, seeRandomNumberDistribution. |
(C++11) | constructs new distribution (public member function)[edit] |
(C++11) | resets the internal state of the distribution (public member function)[edit] |
Generation | |
(C++11) | generates the next random number in the distribution (public member function)[edit] |
Characteristics | |
(C++11) | returns the degrees of freedom (\(\small n\)n) distribution parameter (public member function)[edit] |
(C++11) | gets or sets the distribution parameter object (public member function)[edit] |
(C++11) | returns the minimum potentially generated value (public member function)[edit] |
(C++11) | returns the maximum potentially generated value (public member function)[edit] |
(C++11)(C++11)(removed in C++20) | compares two distribution objects (function)[edit] |
(C++11) | performs stream input and output on pseudo-random number distribution (function template)[edit] |
#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 and0< BarWidth and0<= Padding and0<= 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
| 1. | Weisstein, Eric W. "Chi-Squared Distribution." From MathWorld — A Wolfram Web Resource. |
| 2. | Chi-squared distribution — From Wikipedia. |
