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std:: normal_distribution

From cppreference.net
C++
Numerics library
Pseudo-random number generation
Random number distributions
Uniform distributions
(C++11)
(C++11)
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Bernoulli distributions
(C++11)
(C++11)
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(C++11)
Poisson distributions
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Normal distributions
normal_distribution
(C++11)
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(C++11)
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Sampling distributions
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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:

f(x; μ,σ) =
1
σ √ 2π
exp ⎛
⎜
⎝
-1
2
⎛
⎜
⎝
x-μ
σ
⎞
⎟
⎠ 2
⎞
⎟
⎠

Here μ is the Mean and σ is the Standard deviation ( stddev ).

std::normal_distribution satisfies all requirements of RandomNumberDistribution .

Contents

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
(C++11)
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

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::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.