std::poisson_distribution (3) - Linux Manuals

std::poisson_distribution: std::poisson_distribution


std::poisson_distribution - std::poisson_distribution


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) =


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

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

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


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


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

Non-member functions

           compares two distribution objects
operator== (function)
           performs stream input and output on pseudo-random number distribution
operator<< (function template)


// 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) {
      for(auto p : hist) {
          std::cout << p.first <<
                  ' ' << std::string(p.second/100, '*') << '\n';


  0 *
  1 *******
  2 **************
  3 *******************
  4 *******************
  5 ***************
  6 **********
  7 *****
  8 **
  9 *

External links

Weisstein,_Eric_W._"Poisson_Distribution." From MathWorld--A Wolfram Web Resource.