/C++

# 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

 operator==operator!= (C++11)(C++11)(removed in C++20) compares two distribution objects (function) operator<> (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