NAME¶

std::gamma_distribution - std::gamma_distribution

Synopsis¶

Defined in header <random>
template< class RealType = double > (since C++11)
class gamma_distribution;

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 constructs new distribution
(C++11) (public member function)
reset resets the internal state of the distribution
(C++11) (public member function)

Generation¶

operator() generates the next random number in the distribution
(C++11) (public member function)

Characteristics¶

alpha returns the distribution parameters
beta (public member function)
(C++11)
param gets or sets the distribution parameter object
(C++11) (public member function)
min returns the minimum potentially generated value
(C++11) (public member function)
max returns the maximum potentially generated value
(C++11) (public member function)

Non-member functions¶

operator==
operator!= compares two distribution objects
(C++11) (function)
(C++11)(removed in C++20)
operator<< performs stream input and output on pseudo-random number
operator>> distribution
(C++11) (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.