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# std::poisson_distribution

From cppreference.com
< cpp‎ | numeric‎ | random

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|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.

### [edit] Member types

Member type | Definition
`result_type` | IntType
`param_type` | the type of the parameter set, unspecified

### [edit] Member functions

(constructor) | constructs new distribution (public member function) [edit]
reset | resets the internal state of the distribution (public member function) [edit]
##### Generation
operator() | generates the next random number in the distribution (public member function) [edit]
##### Characteristics
mean | returns the mean distribution parameter (mean number of occurrences of the event) (public member function) [edit]
param | gets or sets the distribution parameter object (public member function) [edit]
min | returns the minimum potentially generated value (public member function) [edit]
max | returns the maximum potentially generated value (public member function) [edit]

### [edit] Non-member functions

operator==operator!= | compares two distribution objects (function) [edit]
operator<<operator>> | performs stream input and output on pseudo-random number distribution (function) [edit]

### [edit] 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

### [edit] External links

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

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