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binomial_distribution Class

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Generates a binomial distribution.

Syntax

template<class IntType = int>
class binomial_distribution
   {
public:
   // types
   typedef IntType result_type;
   struct param_type;

   // constructors and reset functions
   explicit binomial_distribution(result_type t = 1, double p = 0.5);
   explicit binomial_distribution(const param_type& parm);
   void reset();

   // generating functions
   template <class URNG>
   result_type operator()(URNG& gen);
   template <class URNG>
   result_type operator()(URNG& gen, const param_type& parm);

   // property functions
   result_type t() const;
   double p() const;
   param_type param() const;
   void param(const param_type& parm);
   result_type min() const;
   result_type max() const;
   };

Parameters

IntType
The integer result type, defaults to int. For possible types, see <random>.

URNG
The uniform random number generator engine. For possible types, see <random>.

Remarks

The class template describes a distribution that produces values of a user-specified integral type, or type int if none is provided, distributed according to the Binomial Distribution discrete probability function. The following table links to articles about individual members.

binomial_distribution
param_type

The property members t() and p() return the currently stored distribution parameter values t and p respectively.

The property member param() sets or returns the param_type stored distribution parameter package.

The min() and max() member functions return the smallest possible result and largest possible result, respectively.

The reset() member function discards any cached values, so that the result of the next call to operator() does not depend on any values obtained from the engine before the call.

The operator() member functions return the next generated value based on the URNG engine, either from the current parameter package, or the specified parameter package.

For more information about distribution classes and their members, see <random>.

For detailed information about the binomial distribution discrete probability function, see the Wolfram MathWorld article Binomial Distribution.

Example

// compile with: /EHsc /W4
#include <random>
#include <iostream>
#include <iomanip>
#include <string>
#include <map>

void test(const int t, const double p, const int& s) {

    // uncomment to use a non-deterministic seed
    //    std::random_device rd;
    //    std::mt19937 gen(rd());
    std::mt19937 gen(1729);

    std::binomial_distribution<> distr(t, p);

    std::cout << std::endl;
    std::cout << "p == " << distr.p() << std::endl;
    std::cout << "t == " << distr.t() << std::endl;

    // generate the distribution as a histogram
    std::map<int, int> histogram;
    for (int i = 0; i < s; ++i) {
        ++histogram[distr(gen)];
    }

    // print results
    std::cout << "Histogram for " << s << " samples:" << std::endl;
    for (const auto& elem : histogram) {
        std::cout << std::setw(5) << elem.first << ' ' << std::string(elem.second, ':') << std::endl;
    }
    std::cout << std::endl;
}

int main()
{
    int    t_dist = 1;
    double p_dist = 0.5;
    int    samples = 100;

    std::cout << "Use CTRL-Z to bypass data entry and run using default values." << std::endl;
    std::cout << "Enter an integer value for t distribution (where 0 <= t): ";
    std::cin >> t_dist;
    std::cout << "Enter a double value for p distribution (where 0.0 <= p <= 1.0): ";
    std::cin >> p_dist;
    std::cout << "Enter an integer value for a sample count: ";
    std::cin >> samples;

    test(t_dist, p_dist, samples);
}

First run:

Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for t distribution (where 0 <= t): 22
Enter a double value for p distribution (where 0.0 <= p <= 1.0): .25
Enter an integer value for a sample count: 100

p == 0.25
t == 22
Histogram for 100 samples:
    1 :
    2 ::
    3 :::::::::::::
    4 ::::::::::::::
    5 :::::::::::::::::::::::::
    6 ::::::::::::::::::
    7 :::::::::::::
    8 ::::::
    9 ::::::
    11 :
    12 :

Second run:

Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for t distribution (where 0 <= t): 22
Enter a double value for p distribution (where 0.0 <= p <= 1.0): .5
Enter an integer value for a sample count: 100

p == 0.5
t == 22
Histogram for 100 samples:
    6 :
    7 ::
    8 :::::::::
    9 ::::::::::
    10 ::::::::::::::::
    11 :::::::::::::::::::
    12 :::::::::::
    13 :::::::::::::
    14 :::::::::::::::
    15 ::
    16 ::

Third run:

Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for t distribution (where 0 <= t): 22
Enter a double value for p distribution (where 0.0 <= p <= 1.0): .75
Enter an integer value for a sample count: 100

p == 0.75
t == 22
Histogram for 100 samples:
    13 ::::
    14 :::::::::::
    15 :::::::::::::::
    16 :::::::::::::::::::::
    17 ::::::::::::::
    18 :::::::::::::::::
    19 :::::::::::
    20 ::::::
    21 :

Requirements

Header: <random>

Namespace: std

binomial_distribution::binomial_distribution

Constructs the distribution.

explicit binomial_distribution(result_type t = 1, double p = 0.5);
explicit binomial_distribution(const param_type& parm);

Parameters

t
The t distribution parameter.

p
The p distribution parameter.

parm
The param_type structure used to construct the distribution.

Remarks

Precondition: 0 ≤ t and 0.0 ≤ p ≤ 1.0

The first constructor constructs an object whose stored p value holds the value p and whose stored t value holds the value t.

The second constructor constructs an object whose stored parameters are initialized from parm. You can obtain and set the current parameters of an existing distribution by calling the param() member function.

binomial_distribution::param_type

Stores all the parameters of the distribution.

struct param_type {
   typedef binomial_distribution<result_type> distribution_type;
   param_type(result_type t = 1, double p = 0.5);
   result_type t() const;
   double p() const;
   .....
   bool operator==(const param_type& right) const;
   bool operator!=(const param_type& right) const;
   };

Parameters

t
The t distribution parameter.

p
The p distribution parameter.

right
The param_type object to compare to this.

Remarks

Precondition: 0 ≤ t and 0.0 ≤ p ≤ 1.0

This structure can be passed to the distribution's class constructor at instantiation, to the param() member function to set the stored parameters of an existing distribution, and to operator() to be used in place of the stored parameters.

See also

<random>