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:

f(x; μ,σ) = 1 σ \sqrt 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

(constructor) (C++11)	constructs new distribution (public member function)
reset (C++11)	resets the internal state of the distribution (public member function)
Generation
operator() (C++11)	generates the next random number in the distribution (public member function)
Characteristics
meanstddev (C++11)	returns the distribution parameters (public member function)
param (C++11)	gets or sets the distribution parameter object (public member function)
min (C++11)	returns the minimum potentially generated value (public member function)
max (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<<operator>> (C++11)	performs stream input and output on pseudo-random number distribution (function template)

Example

Run this code

#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
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{5.0, 2.0};
 
    // draw a sample from the normal distribution and round it to an integer
    auto random_int = [&d, &gen]{ return std::round(d(gen)); };
 
    std::map<int, int> hist{};
    for (int n = 0; n != 10000; ++n)
        ++hist[random_int()];
 
    for (auto [x, y] : hist)
        std::cout << std::setw(2) << x << ' ' << std::string(y / 200, '*') << '\n';
}

Possible output:

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

External links

1.	Weisstein, Eric W. "Normal Distribution." From MathWorld — A Wolfram Web Resource.
2.	Normal distribution — From Wikipedia.

Compiler support
Freestanding and hosted
Language
Standard library
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Metaprogramming library (C++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (C++17)
Regular expressions library (C++11)
Concurrency support library (C++11)
Execution support library (C++26)
Technical specifications
Symbols index
External libraries

Member functions
normal_distribution::normal_distribution (C++11)
normal_distribution::reset (C++11)
Generation
normal_distribution::operator() (C++11)
Characteristics
normal_distribution::meannormal_distribution::stddev (C++11)(C++11)
normal_distribution::param (C++11)
normal_distribution::min (C++11)
normal_distribution::max (C++11)
Non-member functions
operator==operator!= (C++11)(C++11)(until C++20)
operator<<operator>> (C++11)(C++11)