std::normal_distribution

 

C++

Compiler support

Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Diagnostics library

Memory management library

Metaprogramming library (C++11)

General utilities library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Strings library

Text processing library

Numerics library

Date and time library

Input/output library

Filesystem library (C++17)

Concurrency support library (C++11)

Execution control library (C++26)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Data-parallel types (SIMD) (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Bit manipulation (C++20)
Saturation arithmetic (C++26)
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)
C-style checked integer arithmetic
ckd_add (C++26) ckd_sub (C++26)	ckd_mul (C++26)

 

Pseudo-random number generation

Uniform random bit generators   uniform_random_bit_generator (C++20) Random number engines linear_congruential_engine (C++11) mersenne_twister_engine (C++11) subtract_with_carry_engine (C++11) philox_engine (C++26) Random number engine adaptors discard_block_engine (C++11) independent_bits_engine (C++11) shuffle_order_engine (C++11) Predefined random number generators Non-deterministic random numbers random_device (C++11) Utilities generate_canonical (C++11) seed_seq (C++11) Random number algorithms ranges::generate_random (C++26) C random library rand    srand    RAND_MAX

Random number 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)

 

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 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 (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

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.

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