std::normal_distribution

 

C++

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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 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 longdouble.

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]{returnstd::lround(d(gen));};   std::map<long, unsigned> histogram{};for(auto n{10000}; n;--n)++histogram[random_int()];   for(constauto[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.