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## Class template cauchy_distribution

boost::random::cauchy_distribution

## Synopsis

    // In header: <boost/random/cauchy_distribution.hpp>

    template<typename RealType = double>
    class cauchy_distribution {
    public:
      // types
      typedef RealType input_type;
      typedef RealType result_type;

      // member classes/structs/unions

      class param_type {
      public:
        // types
        typedef cauchy_distribution distribution_type;

        // construct/copy/destruct
        explicit param_type(RealType = 0.0, RealType = 1.0);

        // public member functions
        RealType median() const;
        RealType sigma() const;
        RealType a() const;
        RealType b() const;

        // friend functions
        template<typename CharT, typename Traits>
          friend std::basic_ostream< CharT, Traits > &
          operator<<(std::basic_ostream< CharT, Traits > &, const param_type &);
        template<typename CharT, typename Traits>
          friend std::basic_istream< CharT, Traits > &
          operator>>(std::basic_istream< CharT, Traits > &, const param_type &);
        friend bool operator==(const param_type &, const param_type &);
        friend bool operator!=(const param_type &, const param_type &);
      };

      // construct/copy/destruct
      explicit cauchy_distribution(RealType = 0.0, RealType = 1.0);
      explicit cauchy_distribution(const param_type &);

      // public member functions
      RealType median() const;
      RealType sigma() const;
      RealType a() const;
      RealType b() const;
      RealType min() const;
      RealType max() const;
      param_type param() const;
      void param(const param_type &);
      void reset();
      template<typename Engine> result_type operator()(Engine &);
      template<typename Engine>
        result_type operator()(Engine &, const param_type &);

      // friend functions
      template<typename CharT, typename Traits>
        friend std::basic_ostream< CharT, Traits > &
        operator<<(std::basic_ostream< CharT, Traits > &,
                   const cauchy_distribution &);
      template<typename CharT, typename Traits>
        friend std::basic_istream< CharT, Traits > &
        operator>>(std::basic_istream< CharT, Traits > &,
                   const cauchy_distribution &);
      friend bool operator==(const cauchy_distribution &,
                             const cauchy_distribution &);
      friend bool operator!=(const cauchy_distribution &,
                             const cauchy_distribution &);
    };

## Description

The cauchy distribution is a continuous distribution with two parameters, median and sigma.

It has

### `cauchy_distribution` public construct/copy/destruct

1.     explicit cauchy_distribution(RealType median = 0.0, RealType sigma = 1.0);

   Constructs a `cauchy_distribution` with the paramters `median` and `sigma`.

2.     explicit cauchy_distribution(const param_type & param);

   Constructs a `cauchy_distribution` from it's parameters.

### `cauchy_distribution` public member functions

1.     RealType median() const;

   Returns: the "median" parameter of the distribution

2.     RealType sigma() const;

   Returns: the "sigma" parameter of the distribution

3.     RealType a() const;

   Returns: the "median" parameter of the distribution

4.     RealType b() const;

   Returns: the "sigma" parameter of the distribution

5.     RealType min() const;

   Returns the smallest value that the distribution can produce.

6.     RealType max() const;

   Returns the largest value that the distribution can produce.

7.     param_type param() const;

8.     void param(const param_type & param);

9.     void reset();

   Effects: Subsequent uses of the distribution do not depend on values produced by any engine prior to invoking reset.

10.     template<typename Engine> result_type operator()(Engine & eng);

    Returns: A random variate distributed according to the cauchy distribution.

11.     template<typename Engine>
          result_type operator()(Engine & eng, const param_type & param);

    Returns: A random variate distributed according to the cauchy distribution with parameters specified by param.

### `cauchy_distribution` friend functions

1.     template<typename CharT, typename Traits>
         friend std::basic_ostream< CharT, Traits > &
         operator<<(std::basic_ostream< CharT, Traits > & os,
                    const cauchy_distribution & cd);

   Writes the distribution to a `std::ostream`.

2.     template<typename CharT, typename Traits>
         friend std::basic_istream< CharT, Traits > &
         operator>>(std::basic_istream< CharT, Traits > & is,
                    const cauchy_distribution & cd);

   Reads the distribution from a `std::istream`.

3.     friend bool operator==(const cauchy_distribution & lhs,
                              const cauchy_distribution & rhs);

   Returns true if the two distributions will produce identical sequences of values, given equal generators.

4.     friend bool operator!=(const cauchy_distribution & lhs,
                              const cauchy_distribution & rhs);

   Returns true if the two distributions may produce different sequences of values, given equal generators.