binomial_distribution Class

 

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Generates a binomial distribution.

class binomial_distribution  
   {  
   public:  // types  
   typedef IntType result_type;  
   struct param_type;  // constructors and reset functions  
   explicit binomial_distribution(IntType 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  
   IntType 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>.

The template class 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::binomial_distributionbinomial_distribution::tbinomial_distribution::param
binomial_distribution::operator()binomial_distribution::pbinomial_distribution::param_type

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

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.

 // 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 :  

Header: <random>

Namespace: std

Constructs the distribution.

explicit binomial_distribution(IntType 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 parameter 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.

For more information and a code example, see binomial_distribution Class.

Stores all the parameters of the distribution.

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

Parameters

See parent topic binomial_distribution Class.

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.

<random>

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