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std::cauchy_distribution(3)   C++ Standard Libary  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) =

		  b

		  1 +

		  x - a
		  b

		   2

		   -1

	  std::cauchy_distribution  satisfies  all  requirements of RandomNum-
       berDistribution.

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  RandomNum-
       berDistribution.

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  Off-
       set = 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 ) {
		std::cauchy_distribution<float>	d{ x0 /* a */,	/* 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 << "x	= " << x0 << ",	 = " <<	 << ":\n";
		draw_vbars<4,3>(bars);
		for  (int  n : indices)	{ std::cout << "" << std::setw(2) << n
       << "  ";	}
		std::cout << "\n\n";
	    };

	    cauchy(/* x	= */ -2.0f, /*	= */ 0.50f);
	    cauchy(/* x	= */ +0.0f, /*	= */ 1.25f);
	}

Possible output:
	x = -2,	 = 0.5:
						  0.5006

		    0.0076
	-7  -6	-5  -4	-3  -2	-1   0	 1   2	 3

	x = 0,	= 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.

http://cppreference.com		  2022.07.31	   std::cauchy_distribution(3)

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