Difference between revisions of "cpp/numeric/random/gamma distribution"

Revision as of 02:38, 31 July 2019

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

Member types

Member functions

Non-member functions

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';
    }
}

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

External links

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