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## Class template binomial_distribution

boost::random::binomial_distribution

## Synopsis

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

    template<typename IntType = int, typename RealType = double>
    class binomial_distribution {
    public:
      // types
      typedef IntType  result_type;
      typedef RealType input_type;

      // member classes/structs/unions

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

        // construct/copy/destruct
        explicit param_type(IntType = 1, RealType = 0.5);

        // public member functions
        IntType t() const;
        RealType p() 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 > &, param_type &);
        friend bool operator==(const param_type &, const param_type &);
        friend bool operator!=(const param_type &, const param_type &);
      };

      // construct/copy/destruct
      explicit binomial_distribution(IntType = 1, RealType = 0.5);
      explicit binomial_distribution(const param_type &);

      // public member functions
      template<typename URNG> IntType operator()(URNG &) const;
      template<typename URNG> IntType operator()(URNG &, const param_type &) const;
      IntType t() const;
      RealType p() const;
      IntType min() const;
      IntType max() const;
      param_type param() const;
      void param(const param_type &);
      void reset();

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

## Description

The binomial distribution is an integer valued distribution with two parameters, `t` and `p`. The values of the distribution are within the range [0,t].

The distribution function is .

The algorithm used is the BTRD algorithm described in

> "The generation of binomial random variates", Wolfgang Hormann, Journal of Statistical Computation and Simulation, Volume 46, Issue 1 & 2 April 1993 , pages 101 - 110

### `binomial_distribution` public construct/copy/destruct

1.     explicit binomial_distribution(IntType t = 1, RealType p = 0.5);

   Construct a ``binomial_distribution`` object. `t` and `p` are the parameters of the distribution.

   Requires: t >=0 && 0 <= p <= 1

2.     explicit binomial_distribution(const param_type & param);

   Construct an ``binomial_distribution`` object from the parameters.

### `binomial_distribution` public member functions

1.     template<typename URNG> IntType operator()(URNG & urng) const;

   Returns a random variate distributed according to the binomial distribution.

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

   Returns a random variate distributed according to the binomial distribution with parameters specified by `param`.

3.     IntType t() const;

   Returns the `t` parameter of the distribution.

4.     RealType p() const;

   Returns the `p` parameter of the distribution.

5.     IntType min() const;

   Returns the smallest value that the distribution can produce.

6.     IntType 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 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.

### `binomial_distribution` friend functions

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

   Writes the parameters of 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,
                    binomial_distribution & bd);

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

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

   Returns true if the two distributions will produce the same sequence of values, given equal generators.

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

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