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## Class template normal_distribution

boost::random::normal_distribution

## Synopsis

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

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

      // member classes/structs/unions

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

        // public member functions
        explicit param_type(RealType = 0.0, RealType = 1.0);
        RealType mean() const;
        RealType sigma() const;

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

      // public member functions
      explicit normal_distribution(const RealType & = 0.0, const RealType & = 1.0);
      explicit normal_distribution(const param_type &);
      RealType mean() const;
      RealType sigma() 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 URNG> result_type operator()(URNG &, const param_type &);

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

## Description

Instantiations of class template normal_distribution model a random distribution . Such a distribution produces random numbers `x` distributed with probability density function , where mean and sigma are the parameters of the distribution.

The implementation uses the "ziggurat" algorithm, as described in

> "The Ziggurat Method for Generating Random Variables", George Marsaglia and Wai Wan Tsang, Journal of Statistical Software, Volume 5, Number 8 (2000), 1-7.

### `normal_distribution` public member functions

1.     explicit normal_distribution(const RealType & mean = 0.0,
                                    const RealType & sigma = 1.0);

   Constructs a `normal_distribution` object. `mean` and `sigma` are the parameters for the distribution.

   Requires: sigma >= 0

2.     explicit normal_distribution(const param_type & param);

   Constructs a `normal_distribution` object from its parameters.

3.     RealType mean() const;

   Returns the mean of the distribution.

4.     RealType sigma() const;

   Returns the standard deviation 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;

   Returns the parameters of the distribution.

8.     void param(const param_type & param);

   Sets the parameters of the distribution.

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 normal variate.

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

    Returns a normal variate with parameters specified by `param`.

### `normal_distribution` friend functions

1.     template<typename CharT, typename Traits>
         std::basic_ostream< CharT, Traits > &
         operator<<(std::basic_ostream< CharT, Traits > & os,
                    const normal_distribution & nd);

   Writes a `normal_distribution` to a `std::ostream`.

2.     template<typename CharT, typename Traits>
         std::basic_istream< CharT, Traits > &
         operator>>(std::basic_istream< CharT, Traits > & is,
                    const normal_distribution & nd);

   Reads a `normal_distribution` from a `std::istream`.

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

   Returns true if the two instances of `normal_distribution` will return identical sequences of values given equal generators.

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

   Returns true if the two instances of `normal_distribution` will return different sequences of values given equal generators.