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

class template

std::normal_distribution

template <class RealType = double> class normal_distribution;

Normal distribution

Random number distribution that produces floating-point values according to a normal distribution, which is described by the following probability density function:

This distribution produces random numbers around the distribution mean (μ) with a specific standard deviation (σ).

The normal distribution is a common distribution used for many kind of processes, since it is the distribution that the aggregation of a large number of independent random variables approximates to, when all follow the same distribution (no matter which distribution).

The distribution parameters, mean (μ) and stddev (σ), are set on construction.

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

Template parameters

RealType: A floating-point type. Aliased as member type result_type.
By default, this is double.

Member types The following aliases are member types of normal_distribution:

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

Member functions

(constructor): Construct normal 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:

normal_distribution::mean: Distribution mean (public member function)

normal_distribution::stddev: Standard deviation (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

// normal_distribution
#include <iostream>
#include <string>
#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::normal_distribution<double> distribution(5.0,2.0);

  int p[10]={};

  for (int i=0; i<nrolls; ++i) {
    double number = distribution(generator);
    if ((number>=0.0)&&(number<10.0)) ++p[int(number)];
  }

  std::cout << "normal_distribution (5.0,2.0):" << std::endl;

  for (int i=0; i<10; ++i) {
    std::cout << i << "-" << (i+1) << ": ";
    std::cout << std::string(p[i]*nstars/nrolls,'*') << std::endl;
  }

  return 0;
}

Possible output:

normal_distribution (5.0,2.0):
0-1: *
1-2: ****
2-3: *********
3-4: ***************
4-5: ******************
5-6: *******************
6-7: ***************
7-8: ********
8-9: ****
9-10: *