NAME¶

std::poisson_distribution - std::poisson_distribution

Synopsis¶

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

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

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

e-μ
·μi
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 μ.

std::poisson_distribution satisfies RandomNumberDistribution.

Template parameters¶

The result type generated by the generator. The effect is undefined if
IntType - 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 (C++11) IntType
param_type (C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions¶

constructor constructs new distribution
(C++11) (public member function)
reset resets the internal state of the distribution
(C++11) (public member function)

Generation¶

operator() generates the next random number in the distribution
(C++11) (public member function)

Characteristics¶

mean returns the mean distribution parameter (mean number of occurrences of
(C++11) the event)
(public member function)
param gets or sets the distribution parameter object
(C++11) (public member function)
min returns the minimum potentially generated value
(C++11) (public member function)
max returns the maximum potentially generated value
(C++11) (public member function)

Non-member functions¶

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

Example¶

// Run this code

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

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 [x, y] : hist)
std::cout << std::hex << x << ' '
<< std::string(y / 100, '*') << '\n';
}

Possible output:¶

0 *
1 *******
2 **************
3 *******************
4 *******************
5 ***************
6 **********
7 *****
8 **
9 *
a
b
c
d

External links¶

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