# std::normal_distribution

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< cpp‎ | numeric‎ | random

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`

### 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` | RealType
`param_type` | the type of the parameter set, see `RandomNumberDistribution`.

### Member functions

(constructor) | constructs new distribution (public member function)
reset | resets the internal state of the distribution (public member function)

##### Generation

operator() | generates the next random number in the distribution (public member function)

##### Characteristics

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

### Non-member functions

operator==operator!= | compares two distribution objects (function)
operator<<operator>> | performs stream input and output on pseudo-random number distribution (function template)

### Example

Run this code

    #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::fixed << std::setprecision(1) << std::setw(2)
                      << p.first << ' ' << std::string(p.second/200, '*') << '\n';
        }
    }

Output:

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

### External links

- Weisstein, Eric W. "Normal Distribution." From MathWorld--A Wolfram Web Resource.
- Normal Distribution. From Wikipedia.

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