std::binomial_distribution
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binomial_distribution
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std::binomial_distribution
Member functions
Generation
Characteristics
Non-member functions
(C++11)(C++11)(until C++20)
(C++11)(C++11)
Defined in header
<random>
template< class IntType = int >
class binomial_distribution;
(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.
Contents
[edit] 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.
[edit] Member types
Member type
Definition
result_type (C++11)
IntType
[edit] Member functions
Generation
Characteristics
[edit] Non-member functions
(C++11)
(function template) [edit]
[edit] 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 <iomanip> #include <iostream> #include <map> #include <random> #include <string> 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 const& [x, y] : hist) std::cout << x << ' ' << std::string (y / 100, '*') << '\n'; }
Possible output:
0 ****** 1 ************************ 2 ************************************* 3 ************************* 4 ******
[edit] External links
Weisstein, Eric W. "Binomial Distribution." From MathWorld — A Wolfram Web Resource.