std::gamma_distribution(3) | C++ Standard Libary | std::gamma_distribution(3) |
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 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)
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 <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
External links¶
Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource.
2022.07.31 | http://cppreference.com |