/C++

std::chi_squared_distribution

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

(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 ($$\small n$$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)

Non-member functions

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

Example

#include <random>
#include <iomanip>
#include <map>
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>

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((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
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(*cbegin(s)) V; V e : s)
qr.push_back(std::div(std::lerp(V(0), Height*8, (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";
draw_vbars<4,3>(bars);
for (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