NAME¶

std::chi_squared_distribution - std::chi_squared_distribution

Synopsis¶

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

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 constructs new distribution
(C++11) (public member function)
reset resets the internal state of the distribution
(C++11) (public member function)

Generation¶

operator() generates the next random number in the distribution
(C++11) (public member function)

Characteristics¶

n returns the degrees of freedom (\(\small n\)n) distribution parameter
(C++11) (public member function)
param gets or sets the distribution parameter object
(C++11) (public member function)
min returns the minimum potentially generated value
(C++11) (public member function)
max returns the maximum potentially generated value
(C++11) (public member function)

Non-member functions¶

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