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 \sqrt 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
meanstddev	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::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.

Language
Standard Library Headers
Freestanding and hosted implementations
Named requirements
Language support library
Concepts library (C++20)
Diagnostics library
Utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Input/output library
Localizations library
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Filesystem library (C++17)
Technical Specifications

Common mathematical functions
Special mathematical functions
Floating-point environment (C++11)
Complex numbers
Numeric arrays
Pseudo-random number generation
Compile-time rational arithmetic (C++11)
Numeric algorithms
gcd (C++17)
lcm (C++17)
Interpolations
midpoint (C++20)
lerp (C++20)
Generic numeric operations
iota (C++11)
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)
ispow2 (C++20)
ceil2 (C++20)
floor2 (C++20)
log2p1 (C++20)

Uniform random bit generators
UniformRandomBitGenerator (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

Member functions
normal_distribution::normal_distribution
normal_distribution::reset
Generation
normal_distribution::operator()
Characteristics
normal_distribution::meannormal_distribution::stddev
normal_distribution::param
normal_distribution::min
normal_distribution::max
Non-member functions
operator==operator!=
operator<<operator>>