std::chi_squared_distribution

#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);
}

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