std::binomial_distribution (3) - Linux Manuals

std::binomial_distribution: std::binomial_distribution

NAME

std::binomial_distribution - std::binomial_distribution

Synopsis

Defined in header <random>
template< class IntType = int > (since C++11)
class binomial_distribution;

Produces random non-negative integer values i, distributed according to discrete probability function:

      \(P(i|t,p) = \binom{t}{i} \cdot p^i \cdot (1-p)^{t-i}\)P(i|t,p) =⎛
      ⎜
      ⎝t
      i⎞
      ⎟
      ⎠ · pi
      · (1 − p)t−i

The value obtained is the number of successes in a sequence of t yes/no experiments, each of which succeeds with probability p.
std::binomial_distribution satisfies RandomNumberDistribution

Template parameters

IntType - The result type generated by the generator. The effect is undefined if this is not one of short, int, long, long long, unsigned short, unsigned int, unsigned long, or unsigned long long.

Member types

Member type Definition
result_type IntType
param_type the type of the parameter set, see RandomNumberDistribution.

Member functions

              constructs new distribution
constructor (public member function)
              resets the internal state of the distribution
reset (public member function)

Generation

              generates the next random number in the distribution
operator() (public member function)

Characteristics

              returns the distribution parameters
p (public member function)
t
              gets or sets the distribution parameter object
param (public member function)
              returns the minimum potentially generated value
min (public member function)
              returns the maximum potentially generated value
max (public member function)

Non-member functions

           compares two distribution objects
operator== (function)
operator!=
           performs stream input and output on pseudo-random number distribution
operator<< (function template)
operator>>

Example

Plot of binomial distribution with probability of success of each trial exactly 0.5, illustrating the relationship with the pascal triangle (the probabilities that none, 1, 2, 3, or all four of the 4 trials will be successful in this case are 1:4:6:4:1)
// Run this code

  #include <iostream>
  #include <iomanip>
  #include <string>
  #include <map>
  #include <random>

  int main()
  {
      std::random_device rd;
      std::mt19937 gen(rd());
      // perform 4 trials, each succeeds 1 in 2 times
      std::binomial_distribution<> d(4, 0.5);

      std::map<int, int> hist;
      for (int n = 0; n < 10000; ++n) {
          ++hist[d(gen)];
      }
      for (auto p : hist) {
          std::cout << p.first << ' '
                    << std::string(p.second/100, '*') << '\n';
      }
  }

Possible output:

  0 ******
  1 ************************
  2 *************************************
  3 *************************
  4 ******

External links

Weisstein,_Eric_W._"Binomial_Distribution." From MathWorld--A Wolfram Web Resource.