/C++

# std::gamma_distribution

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 RealType
param_type(C++11) the type of the parameter set, see RandomNumberDistribution.

### Member functions

(C++11)
constructs new distribution
(public member function)
(C++11)
resets the internal state of the distribution
(public member function)
##### Generation
(C++11)
generates the next random number in the distribution
(public member function)
##### Characteristics
returns the distribution parameters
(public member function)
(C++11)
gets or sets the distribution parameter object
(public member function)
(C++11)
returns the minimum potentially generated value
(public member function)
(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<> (C++11) performs stream input and output on pseudo-random number distribution (function template)

### Example

#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <random>
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 p : hist) {
if (p.second/100. > 0.5)
std::cout
<< std::fixed << std::setprecision(1)
<< p.first/2.0 << '-' << (p.first+1)/2.0 << ' '
<< std::string(p.second/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

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