# std::gamma_distribution

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< cpp‎ | numeric‎ | random

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
alpha beta (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.

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