std::binomial_distribution

C++

Language

Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Algorithms library

Iterators library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

Numerics library

Common mathematical functions

Special mathematical functions

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

ispow2 (C++20)

ceil2 (C++20)

floor2 (C++20)

log2p1 (C++20)

Pseudo-random number generation

Uniform random bit generators

UniformRandomBitGenerator (C++20)

Engines and engine adaptors

linear_congruential_engine (C++11)

mersenne_twister_engine (C++11)

subtract_with_carry_engine (C++11)

discard_block_engine (C++11)

independent_bits_engine (C++11)

shuffle_order_engine (C++11)

Non-deterministic generator

random_device (C++11)

Distributions

Uniform distributions

uniform_int_distribution (C++11)

uniform_real_distribution (C++11)

generate_canonical (C++11)

Bernoulli distributions

bernoulli_distribution (C++11)

binomial_distribution (C++11)

negative_binomial_distribution (C++11)

geometric_distribution (C++11)

Poisson distributions

poisson_distribution (C++11)

exponential_distribution (C++11)

gamma_distribution (C++11)

weibull_distribution (C++11)

extreme_value_distribution (C++11)

Normal distributions

normal_distribution (C++11)

lognormal_distribution (C++11)

chi_squared_distribution (C++11)

cauchy_distribution (C++11)

fisher_f_distribution (C++11)

student_t_distribution (C++11)

Sampling distributions

discrete_distribution (C++11)

piecewise_constant_distribution (C++11)

piecewise_linear_distribution (C++11)

Seed Sequences

seed_seq (C++11)

C library

rand

srand

RAND_MAX

std::binomial_distribution

Member functions

binomial_distribution::binomial_distribution

binomial_distribution::reset

Generation

binomial_distribution::operator()

Characteristics

binomial_distribution::pbinomial_distribution::t

binomial_distribution::param

binomial_distribution::min

binomial_distribution::max

Non-member functions

operator==operator!=

operator<<operator>>

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

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)ti

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

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

Non-member functions

operator==operator!=	compares two distribution objects (function)
operator<<operator>>	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 <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.