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std::normal_distribution

Defined in header <random>
template< class RealType = double >
class normal_distribution;
(since C++11)

Generates random numbers according to the Normal (or Gaussian) random number distribution. It is defined as: \(\small{f(x;\mu,\sigma)}=\frac{1}{\sigma\sqrt{2\pi} }\exp{(-\frac{1}{2}{(\frac{x-\mu}{\sigma})}^2)}\)f(x; μ,σ) =

1/σ√2π exp

-1/2

x-μ/σ

2


Here \(\small\mu\)μ is the mean and \(\small\sigma\)σ is the standard deviation (stddev).

std::normal_distribution satisfies all requirements of RandomNumberDistribution.

Template parameters

RealType - The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

Member types

Member type Definition
result_type(C++11) RealType
param_type(C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions

(C++11)
constructs new distribution
(public member function)
(C++11)
resets the internal state of the distribution
(public member function)
Generation
(C++11)
generates the next random number in the distribution
(public member function)
Characteristics
returns the distribution parameters
(public member function)
(C++11)
gets or sets the distribution parameter object
(public member function)
(C++11)
returns the minimum potentially generated value
(public member function)
(C++11)
returns the maximum potentially generated value
(public member function)

Non-member functions

(C++11)(C++11)(removed in C++20)
compares two distribution objects
(function)
(C++11)
performs stream input and output on pseudo-random number distribution
(function template)

Example

#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <random>
#include <cmath>
int main()
{
    std::random_device rd{};
    std::mt19937 gen{rd()};
 
    // values near the mean are the most likely
    // standard deviation affects the dispersion of generated values from the mean
    std::normal_distribution<> d{5,2};
 
    std::map<int, int> hist{};
    for(int n=0; n<10000; ++n) {
        ++hist[std::round(d(gen))];
    }
    for(auto p : hist) {
        std::cout << std::setw(2)
                  << p.first << ' ' << std::string(p.second/200, '*') << '\n';
    }
}

Possible output:

-2 
-1 
 0 
 1 *
 2 ***
 3 ******
 4 ********
 5 **********
 6 ********
 7 *****
 8 ***
 9 *
10 
11 
12

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https://en.cppreference.com/w/cpp/numeric/random/normal_distribution