std::gamma_distribution
From cppreference.com
C++
Feature test macros (C++20)
Concepts library (C++20)
Metaprogramming library (C++11)
Ranges library (C++20)
Filesystem library (C++17)
Concurrency support library (C++11)
Execution control library (C++26)
Numerics library
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Data-parallel types (SIMD) (C++26)
Floating-point environment (C++11)
Bit manipulation (C++20)
Saturation arithmetic (C++26)
(C++17)
(C++17)
(C++17)
(C++17)
(C++17)
(C++17)
Pseudo-random number generation
(C++20)
(C++11)
(C++11)
(C++11)
(C++26)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++26)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
gamma_distribution
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
std::gamma_distribution
Member functions
Generation
Characteristics
Non-member functions
(C++11)(C++11)(until C++20)
(C++11)(C++11)
Defined in header
<random>
template< class RealType = double >
class gamma_distribution;
(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/ββα· xα-1
· Γ(α)
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
[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
[edit] Member functions
Generation
Characteristics
[edit] Non-member functions
(C++11)
(function template) [edit]
[edit] 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
[edit] External links
Weisstein, Eric W. "Gamma Distribution." From MathWorld — A Wolfram Web Resource.