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 longdouble.

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

#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::lround(d(gen)); };

    std::map<long, unsigned> histogram{};
    for (auto n{10000}; n; --n)
        ++histogram[random_int()];

    for (const auto [k, v] : histogram)
        std::cout << std::setw(2) << k << ' ' << std::string(v / 200, '*') << '\n';
}

Possible output:

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

External links

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

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