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Showing content from https://cplusplus.com/reference/random/poisson_distribution/ below:

class template

std::poisson_distribution

template <class IntType = int> class poisson_distribution;

Poisson distribution

Random number distribution that produces integers according to a Poisson distribution, which is described by the following probability mass function:

This distribution produces random integers where each value represents a specific count of independent events occurring within a fixed interval, based on the observed mean rate at which they appear to happen (μ).

The distribution parameter, mean (μ), is set on construction.

To produce a random value following this distribution, call its member function operator().

Template parameters

IntType: An integer type. Aliased as member type result_type.
By default, this is int.

Member types The following aliases are member types of poisson_distribution:

member type definition notes result_type The first template parameter (IntType) The type of the numbers generated (defaults to int) param_type not specified The type returned by member param.

Member functions

(constructor): Construct Poisson distribution (public member function)

operator(): Generate random number (public member function)

reset: Reset distribution (public member function)

param: Distribution parameters (public member function)

min: Minimum value (public member function)

max: Maximum value (public member function)

Distribution parameters

mean: Mean (public member function)

Non-member functions

operator<<: Insert into output stream (function template)

operator>>: Extract from input stream (function template)

relational operators: Relational operators (function template)

Example

// poisson_distribution
#include <iostream>
#include <random>

int main()
{
  const int nrolls = 10000; // number of experiments
  const int nstars = 100;   // maximum number of stars to distribute

  std::default_random_engine generator;
  std::poisson_distribution<int> distribution(4.1);

  int p[10]={};

  for (int i=0; i<nrolls; ++i) {
    int number = distribution(generator);
    if (number<10) ++p[number];
  }

  std::cout << "poisson_distribution (mean=4.1):" << std::endl;
  for (int i=0; i<10; ++i)
    std::cout << i << ": " << std::string(p[i]*nstars/nrolls,'*') << std::endl;

  return 0;
}

Possible output:

poisson_distribution (mean=4.1):
0: *
1: ******
2: *************
3: *******************
4: *******************
5: ***************
6: ***********
7: ******
8: ***
9: *