template<classRealType=double>classchi_squared_distribution;(since C++11)The chi_squared_distribution produces random numbers x>0 according to the
:
f(x;n) = x(n/2)-1
e-x/2Γ(n/2) 2n/2
Γ is the
(See also
) and n are the
(default 1).
satisfies all requirements of
.
Template parameters
RealType - The result type generated by the generator. The effect is undefined if this is not one of float, double, or longdouble. Member types
Member type Definition result_type(C++11)RealTypeparam_typethe type of the parameter set, see
. Member functions
constructs new distribution
(public member function)
resets the internal state of the distribution
(public member function)
Generation
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)
gets or sets the distribution parameter object
(public member function)
returns the minimum potentially generated value
(public member function)
returns the maximum potentially generated value
(public member function)
Non-member functions
Example
Run this code
#include<algorithm>#include<cmath>#include<iomanip>#include<iostream>#include<map>#include<random>#include<vector>template<intHeight=5,intBarWidth=1,intPadding=1,intOffset=0,classSeq>voiddraw_vbars(Seq&&s,constboolDrawMinMax=true){static_assert(0<Heightand0<BarWidthand0<=Paddingand0<=Offset);autocout_n=[](auto&&v,intn=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(typedefdecltype(*std::cbegin(s))V;Ve:s)qr.push_back(std::div(std::lerp(V(0),8*Height,(e-*min)/(*max-*min)),8));for(autoh{Height};h-->0;cout_n('\n')){cout_n(' ',Offset);for(autodv:qr){constautoq{dv.quot},r{dv.rem};unsignedchard[]{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;}}intmain(){std::random_devicerd{};std::mt19937gen{rd()};autoχ2=[&gen](constfloatdof){std::chi_squared_distribution<float>d{dof/* n */};constintnorm=1'00'00;constfloatcutoff=0.002f;std::map<int,int>hist{};for(intn=0;n!=norm;++n)++hist[std::round(d(gen))];std::vector<float>bars;std::vector<int>indices;for(autoconst&[n,p]:hist)if(floatx=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);intn:indices)std::cout<<std::setw(2)<<n<<" ";std::cout<<"\n\n";};for(floatdof:{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 External links