NAME¶

std::normal_distribution - std::normal_distribution

Synopsis¶

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

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¶

constructor constructs new distribution
(C++11) (public member function)
reset resets the internal state of the distribution
(C++11) (public member function)

Generation¶

operator() generates the next random number in the distribution
(C++11) (public member function)

Characteristics¶

mean returns the distribution parameters
stddev (public member function)
(C++11)
param gets or sets the distribution parameter object
(C++11) (public member function)
min returns the minimum potentially generated value
(C++11) (public member function)
max returns the maximum potentially generated value
(C++11) (public member function)

Non-member functions¶

operator==
operator!= compares two distribution objects
(C++11) (function)
(C++11)(removed in C++20)
operator<< performs stream input and output on pseudo-random number
operator>> distribution
(C++11) (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.