std::gamma_distribution

 

C++

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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::gamma_distribution

Member functions

gamma_distribution::gamma_distribution

gamma_distribution::reset

Generation

gamma_distribution::operator()

Characteristics

gamma_distribution::alphagamma_distribution::beta

gamma_distribution::param

gamma_distribution::min

gamma_distribution::max

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 gamma_distribution;		(since C++11)

Produces random positive floating-point values x, distributed according to probability density function:

\(\mathsf{p}(x\mid\alpha,\beta) = \frac{e^{-x/\beta} }{\beta^\alpha\cdot\Gamma(\alpha)}\cdot x^{\alpha-1} \)P(x|α,β) =

e-x/β

βα · Γ(α)

· xα-1

where α is known as the shape parameter and β is known as the scale parameter. The shape parameter is sometimes denoted by the letter k and the scale parameter is sometimes denoted by the letter θ.

For floating-point α, the value obtained is the sum of α independent exponentially distributed random variables, each of which has a mean of β.

std::gamma_distribution satisfies 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
alphabeta (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 <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
int main()
{
    std::random_device rd;
    std::mt19937 gen(rd());
 
    // A gamma distribution with alpha = 1, and beta = 2
    // approximates an exponential distribution.
    std::gamma_distribution<> d(1, 2);
 
    std::map<int, int> hist;
    for (int n = 0; n != 10000; ++n)
        ++hist[2 * d(gen)];
 
    for (auto const& [x, y] : hist)
        if (y / 100.0 > 0.5)
            std::cout << std::fixed << std::setprecision(1)
                      << x / 2.0 << '-' << (x + 1) / 2.0 << ' '
                      << std::string(y / 100, '*') << '\n';
}

Possible output:

0.0-0.5 **********************
0.5-1.0 ****************
1.0-1.5 *************
1.5-2.0 **********
2.0-2.5 ********
2.5-3.0 ******
3.0-3.5 *****
3.5-4.0 ****
4.0-4.5 ***
4.5-5.0 **
5.0-5.5 **
5.5-6.0 *
6.0-6.5 *
6.5-7.0
7.0-7.5
7.5-8.0

External links

Weisstein, Eric W. "Gamma Distribution." From MathWorld — A Wolfram Web Resource.