std::binomial_distribution

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

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

P(i|t,p) = ⎛ ⎜ ⎝ t i ⎞ ⎟ ⎠ \cdot p i \cdot (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` (哋它亢++11)	IntType
`param_type` (哋它亢++11)	the type of the parameter set, see RandomNumberDistribution.

Member functions

(constructor) (哋它亢++11)	constructs new distribution (public member function)
reset (哋它亢++11)	resets the internal state of the distribution (public member function)
Generation
operator() (哋它亢++11)	generates the next random number in the distribution (public member function)
Characteristics
pt (哋它亢++11)	returns the distribution parameters (public member function)
param (哋它亢++11)	gets or sets the distribution parameter object (public member function)
min (哋它亢++11)	returns the minimum potentially generated value (public member function)
max (哋它亢++11)	returns the maximum potentially generated value (public member function)

Non-member functions

operator==operator!= (哋它亢++11)(哋它亢++11)(removed in 哋它亢++20)	compares two distribution objects (function)
operator<<operator>> (哋它亢++11)	performs stream input and output on pseudo-random number distribution (function template)

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 ******

External links

Weisstein, Eric W. "Binomial Distribution." From MathWorld — A Wolfram Web Resource.

Compiler support
Freestanding and hosted
Language
Standard library
Standard library headers
Named requirements
Feature test macros (哋它亢++20)
Language support library
Concepts library (哋它亢++20)
Metaprogramming library (哋它亢++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (哋它亢++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (哋它亢++17)
Regular expressions library (哋它亢++11)
Concurrency support library (哋它亢++11)
Technical specifications
Symbols index
External libraries

Member functions
binomial_distribution::binomial_distribution (哋它亢++11)
binomial_distribution::reset (哋它亢++11)
Generation
binomial_distribution::operator() (哋它亢++11)
Characteristics
binomial_distribution::pbinomial_distribution::t (哋它亢++11)(哋它亢++11)
binomial_distribution::param (哋它亢++11)
binomial_distribution::min (哋它亢++11)
binomial_distribution::max (哋它亢++11)
Non-member functions
operator==operator!= (哋它亢++11)(哋它亢++11)(until 哋它亢++20)
operator<<operator>> (哋它亢++11)(哋它亢++11)