std::gamma_distribution - cppreference.com (original) (raw)
| | | | | ---------------------------------------------------------------- | | ------------- | | 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) = · 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.
Contents
- 1 Template parameters
- 2 Member types
- 3 Member functions
- 4 Non-member functions
- 5 Example
- 6 External links
[edit] 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. |
|---|
[edit] Member types
| Member type | Definition |
|---|---|
| result_type (C++11) | RealType |
| param_type (C++11) | the type of the parameter set, see RandomNumberDistribution. |
[edit] Member functions
| (constructor)(C++11) | constructs new distribution (public member function) [edit] |
|---|---|
| reset(C++11) | resets the internal state of the distribution (public member function) [edit] |
| Generation | |
| operator()(C++11) | generates the next random number in the distribution (public member function) [edit] |
| Characteristics | |
| alphabeta(C++11) | returns the distribution parameters (public member function) [edit] |
| param(C++11) | gets or sets the distribution parameter object (public member function) [edit] |
| min(C++11) | returns the minimum potentially generated value (public member function) [edit] |
| max(C++11) | returns the maximum potentially generated value (public member function) [edit] |
[edit] Non-member functions
[edit] Example
#include #include #include #include #include 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