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std::gamma_distribution

From cppreference.com
< cpp‎ | numeric‎ | random
 
 
 
Pseudo-random number generation
Uniform random bit generators
Engines and engine adaptors
Non-deterministic generator
Distributions
Uniform distributions
Bernoulli distributions
Poisson distributions
gamma_distribution
(C++11)
Normal distributions
Sampling distributions
Seed Sequences
(C++11)
C library
 
 
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:

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

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 RealType
param_type the type of the parameter set, see RandomNumberDistribution.

[edit] Member functions

constructs new distribution
(public member function) [edit]
resets the internal state of the distribution
(public member function) [edit]
Generation
generates the next random number in the distribution
(public member function) [edit]
Characteristics
returns the distribution parameters
(public member function) [edit]
gets or sets the distribution parameter object
(public member function) [edit]
returns the minimum potentially generated value
(public member function) [edit]
returns the maximum potentially generated value
(public member function) [edit]

[edit] Non-member functions

compares two distribution objects
(function) [edit]
performs stream input and output on pseudo-random number distribution
(function template) [edit]

[edit] 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) {
        std::cout << std::fixed << std::setprecision(1) 
                  << p.first/2.0 << '-' << (p.first+1)/2.0 <<
                ' ' << std::string(p.second/200, '*') << '\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 
8.0-8.5 
8.5-9.0 
9.0-9.5 
9.5-10.0 
10.0-10.5 
10.5-11.0 
11.0-11.5 
11.5-12.0 
12.0-12.5 
12.5-13.0 
13.0-13.5 
13.5-14.0 
14.0-14.5 
15.0-15.5 
15.5-16.0 
18.0-18.5 
18.5-19.0

[edit] External links

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