std::poisson_distribution

C++

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Technical Specifications

Numerics library

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accumulate

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transform_exclusive_scan (C++17)

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bit_cast (C++20)

ispow2 (C++20)

ceil2 (C++20)

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Pseudo-random number generation

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UniformRandomBitGenerator (C++20)

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linear_congruential_engine (C++11)

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Non-deterministic generator

random_device (C++11)

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uniform_int_distribution (C++11)

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generate_canonical (C++11)

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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::poisson_distribution

Member functions

poisson_distribution::poisson_distribution

poisson_distribution::reset

Generation

poisson_distribution::operator()

Characteristics

poisson_distribution::mean

poisson_distribution::param

poisson_distribution::min

poisson_distribution::max

Non-member functions

operator==operator!=

operator<<operator>>

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

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

\(P(i | \mu) = \frac{e^{-\mu}\mu^i}{i!}\)P(i|) =

e- i

i!

The value obtained is the probability of exactly i occurrences of a random event if the expected, mean number of its occurrence under the same conditions (on the same time/space interval) is .

std::poisson_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
mean	returns the mean distribution parameter (mean number of occurrences of the event) (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

Run this code

#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <random>
int main()
{
    std::random_device rd;
    std::mt19937 gen(rd());

    // if an event occurs 4 times a minute on average
    // how often is it that it occurs n times in one minute?
    std::poisson_distribution<> d(4);

    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';
    }
}

Output:

0 *
1 *******
2 **************
3 *******************
4 *******************
5 ***************
6 **********
7 *****
8 **
9 *
10 
11 
12 
13

External links

Weisstein, Eric W. "Poisson Distribution." From MathWorld--A Wolfram Web Resource.