std::normal_distribution

 

C++

Compiler support

Freestanding and hosted

Language

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)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions

Mathematical special functions (C++17)

Mathematical constants (C++20)

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Factor operations

gcd (C++17)

lcm (C++17)

Interpolations

midpoint (C++20)

lerp (C++20)

Generic numeric operations

iota (C++11)

ranges::iota (C++23)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

byteswap (C++23)

has_single_bit (C++20)

bit_ceil (C++20)

bit_floor (C++20)

bit_width (C++20)

rotl (C++20)

rotr (C++20)

countl_zero (C++20)

countl_one (C++20)

countr_zero (C++20)

countr_one (C++20)

popcount (C++20)

endian (C++20)

 

Pseudo-random number generation

Uniform random bit generators

uniform_random_bit_generator (C++20)

Engines and engine adaptors

linear_congruential_engine (C++11)

mersenne_twister_engine (C++11)

subtract_with_carry_engine (C++11)

discard_block_engine (C++11)

independent_bits_engine (C++11)

shuffle_order_engine (C++11)

Non-deterministic generator

random_device (C++11)

Distributions

Uniform distributions

uniform_int_distribution (C++11)

uniform_real_distribution (C++11)

generate_canonical (C++11)

Bernoulli distributions

bernoulli_distribution (C++11)

binomial_distribution (C++11)

negative_binomial_distribution (C++11)

geometric_distribution (C++11)

Poisson distributions

poisson_distribution (C++11)

exponential_distribution (C++11)

gamma_distribution (C++11)

weibull_distribution (C++11)

extreme_value_distribution (C++11)

Normal distributions

normal_distribution (C++11)

lognormal_distribution (C++11)

chi_squared_distribution (C++11)

cauchy_distribution (C++11)

fisher_f_distribution (C++11)

student_t_distribution (C++11)

Sampling distributions

discrete_distribution (C++11)

piecewise_constant_distribution (C++11)

piecewise_linear_distribution (C++11)

Seed Sequences

seed_seq (C++11)

C library

rand

srand

RAND_MAX

 

std::normal_distribution

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)

 

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

Possible 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.