std::poisson_distribution(3)

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 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
                 returns the mean distribution parameter (mean number of occurrences of
   mean 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 <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 << std::hex << p.first << ' '
                   << std::string(p.second/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.