std::chi_squared_distribution

 

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std::chi_squared_distribution

Member functions

chi_squared_distribution::chi_squared_distribution

chi_squared_distribution::reset

Generation

chi_squared_distribution::operator()

Characteristics

chi_squared_distribution::n

chi_squared_distribution::param

chi_squared_distribution::min

chi_squared_distribution::max

Non-member functions

operator==operator!= (C++11)(C++11)(until C++20)

operator<<operator>> (C++11)(C++11)

 

Defined in header <random>
template< class RealType = double > class chi_squared_distribution;		(since C++11)

The chi_squared_distribution produces random numbers \(\small x>0\)x>0 according to the Chi-squared distribution:

\({\small f(x;n) = }\frac{x^{(n/2)-1}\exp{(-x/2)} }{\Gamma{(n/2)}2^{n/2} }\)f(x;n) =

x(n/2)-1 e-x/2

Γ(n/2) 2n/2

\(\small\Gamma\)Γ is the Gamma function (See also std::tgamma) and \(\small n\)n are the degrees of freedom (default 1).

std::chi_squared_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 (C++11)	RealType
param_type (C++11)	the type of the parameter set, see RandomNumberDistribution.

Member functions

(constructor) (C++11)	constructs new distribution (public member function)
reset (C++11)	resets the internal state of the distribution (public member function)
Generation
operator() (C++11)	generates the next random number in the distribution (public member function)
Characteristics
n (C++11)	returns the degrees of freedom (\(\small n\)n) distribution parameter (public member function)
param (C++11)	gets or sets the distribution parameter object (public member function)
min (C++11)	returns the minimum potentially generated value (public member function)
max (C++11)	returns the maximum potentially generated value (public member function)

Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20)	compares two distribution objects (function)
operator<<operator>> (C++11)	performs stream input and output on pseudo-random number distribution (function template)

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, const bool 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;
    };
 
    const auto [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)
        {
            const auto q{dv.quot}, r{dv.rem};
            unsigned char 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](const float dof)
    {
        std::chi_squared_distribution<float> d{dof /* n */};
 
        const int norm = 1'00'00;
        const float 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 (auto const& [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

External links

	Weisstein, Eric W. "Chi-Squared Distribution." From MathWorld — A Wolfram Web Resource.
	Chi-squared distribution — From Wikipedia.