std::cauchy_distribution(3)

NAME
std::cauchy_distribution - std::cauchy_distribution

Synopsis
   Defined in header <random>
   template< class RealType = double > (since C++11)
   class cauchy_distribution;
   Produces random numbers according to a Cauchy distribution (also called Lorentz
   distribution):
           \({\small f(x;a,b)={(b\pi{[1+{(\frac{x-a}{b})}^{2}]} })}^{-1}\)f(x; a,b) =
           ⎛
           ⎜
           ⎝bπ ⎡
           ⎢
           ⎣1 + ⎛
           ⎜
           ⎝
           x - a
           b
           ⎞
           ⎟
           � 2
           ⎤
           ⎥
           ⎦⎞
           ⎟
           � -1
   std::cauchy_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
   a returns the distribution parameters
   b (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 <random>
 #include <map>
 #include <iomanip>
 #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 cauchy = [&gen](const float x0, const float 𝛾) {
         std::cauchy_distribution<float> d{ x0 /* a */, 𝛾 /* b */};
         const int norm = 1'00'00;
         const float cutoff = 0.005f;
         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 << "x₀ = " << x0 << ", 𝛾 = " << 𝛾 << ":\n";
         draw_vbars<4,3>(bars);
         for (int n : indices) { std::cout << "" << std::setw(2) << n << " "; }
         std::cout << "\n\n";
     };
     cauchy(/* x₀ = */ -2.0f, /* 𝛾 = */ 0.50f);
     cauchy(/* x₀ = */ +0.0f, /* 𝛾 = */ 1.25f);
 }

Possible output:
 x₀ = -2, 𝛾 = 0.5:
                     ███ ┬ 0.5006
                     ███ │
                 ▂▂▂ ███ ▁▁▁ │
 ▁▁▁ ▁▁▁ ▁▁▁ ▃▃▃ ███ ███ ███ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0076
 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
 x₀ = 0, 𝛾 = 1.25:
                        ███ ┬ 0.2539
                        ▅▅▅ ███ ▃▃▃ │
                        ▁▁▁ ███ ███ ███ ▁▁▁ │
 ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▃▃▃ ▅▅▅ ███ ███ ███ ███ ███ ▅▅▅ ▃▃▃ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0058
 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 9

External links
   Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource.